Chà, thật hữu ích khi biết đó là Định lý Pythagoras với một cái gì đó bổ sung để nó hoạt động cho mọi tam giác
Định lý Py-ta-go
[chỉ dành cho Tam giác vuông] a2 + b2 = c2
Định luật Côsin
[cho mọi tam giác]a2 + b2 − 2ab cos[C] = c2
Vì vậy, để ghi nhớ nó
- nghĩ "abc". a2 + b2 = c2,
- sau đó là "abc" thứ 2. 2ab cos[C],
- và đặt chúng lại với nhau. a2 + b2 − 2ab cos[C] = c2
Khi nào nên sử dụng
Luật Cosines rất hữu ích cho việc tìm kiếm
- cạnh thứ ba của tam giác khi biết hai cạnh và góc xen giữa [như ví dụ trên]
- các góc của tam giác khi biết cả ba cạnh [như ví dụ sau]
Thí dụ. Góc "C" là gì. ?
Cạnh có độ dài "8" đối diện với góc C nên nó là cạnh c. Hai cạnh còn lại là a và b
Bây giờ chúng ta hãy đưa những gì chúng ta biết vào Định luật Cosines
Bắt đầu với. c2 = a2 + b2 − 2ab cos[C]
Điền vào a, b và c. 82 = 92 + 52 − 2 × 9 × 5 × cos[C]
Tính toán. 64 = 81 + 25 − 90 × cos[C]
Bây giờ chúng ta sử dụng các kỹ năng đại số của mình để sắp xếp lại và giải quyết
Trừ 25 từ cả hai vế. 39 = 81 − 90 × cos[C]
Trừ 81 từ cả hai phía. −42 = −90 × cos[C]
đổi bên. −90 × cos[C] = −42
Chia cả hai vế cho −90. cos[C] = 42/90
nghịch đảo cosin. C = cos−1[42/90]
Máy tính. C = 62. 2° [đến 1 chữ số thập phân]
Ở Các Hình Thức Khác
Phiên bản dễ dàng hơn cho các góc
Chúng ta vừa xem cách tìm một góc khi biết ba cạnh. Phải mất khá nhiều bước, do đó, việc sử dụng công thức "trực tiếp" sẽ dễ dàng hơn [chỉ là sự sắp xếp lại của công thức c2 = a2 + b2 − 2ab cos[C]]. Nó có thể ở một trong hai dạng này
cos[C] = a2 + b2 − c2 2ab
cos[A] = b2 + c2 − a2 2bc
cos[B] = c2 + a2 − b2 2ca
Thí dụ. Tìm Góc "C" Sử Dụng Định Luật Côsin [phiên bản góc]
Trong tam giác này, chúng ta biết ba cạnh
Sử dụng Định luật Côsin [phiên bản góc] để tìm góc C
= 57. 9° đến một chữ số thập phân
Phiên bản cho a, b và c
Ngoài ra, chúng ta có thể viết lại công thức c2 = a2 + b2 − 2ab cos[C] thành dạng a2= và b2=
Đây là cả ba
a2 = b2 + c2 − 2bc cos[A]
b2 = a2 + c2 − 2ac cos[B]
c2 = a2 + b2 − 2ab cos[C]
Nhưng việc nhớ dạng "c2=" và thay đổi các chữ cái khi cần thiết sẽ dễ dàng hơn
Như trong ví dụ này
Thí dụ. Tìm khoảng cách "z"
Các chữ cái là khác nhau. Nhưng điều đó không quan trọng. Chúng ta có thể dễ dàng thay thế x cho a, y cho b và z cho c
Bắt đầu với. c2 = a2 + b2 − 2ab cos[C]
x cho a, y cho b và z cho cz2 = x2 + y2 − 2xy cos[Z]
Đặt trong các giá trị chúng ta biết. z2 = 9. 42 + 6. 52 − 2×9. 4x6. 5×cos[131º]
Tính toán. z2 = 88. 36 + 42. 25 − 122. 2 × [−0. 656. ]
z = √210. 78. = 14. 5 đến 1 chữ số thập phân
Câu trả lời. z = 14. 5
Bạn có nhận thấy rằng cos[131º] là số âm và điều này thay đổi dấu cuối cùng trong phép tính thành + [cộng] không?
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
c^2 = a^2 + b^2 - 2[a][b][cos beta]7_______0_______6_______0_______9_______0_______6
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]1
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
c^2 = a^2 + b^2 - 2[a][b][cos beta]9
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]5
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]6
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]9
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.2
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.4
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.5
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.6
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.8
c^2 = a^2 + b^2 - 2[a][b][cos beta]6_______0_______9
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
alpha : 90 beta : 45 gamma : 452
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
c^2 = a^2 + b^2 - 2[a][b][cos beta]9_______0_______6
alpha : 90 beta : 45 gamma : 456
alpha : 90 beta : 45 gamma : 457
alpha : 90 beta : 45 gamma : 458
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
c^2 = a^2 + b^2 - 2[a][b][cos beta]9_______0_______6
// Code to find all three angles
2beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]6
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
// Code to find all three angles
5beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
// Code to find all three angles
8beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
// of a triangle given coordinate
1beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
// of a triangle given coordinate
4
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
// of a triangle given coordinate
6beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
// of a triangle given coordinate
8 // of a triangle given coordinate
9// of all three vertices
0// of all three vertices
1beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
// of a triangle given coordinate
8 // of all three vertices
4// of all three vertices
0// of all three vertices
6beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
// of a triangle given coordinate
8 // of all three vertices
9// of all three vertices
0#include
1
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
#include
3beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
// of a triangle given coordinate
8 #include
6#include
7#include
8beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
// of a triangle given coordinate
8 #include // for pair
1#include
7#include // for pair
3beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
// of a triangle given coordinate
8 #include // for pair
6#include
7#include // for pair
8
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]00
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]02
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]04
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]06
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]08
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]10_______0_______11
c^2 = a^2 + b^2 - 2[a][b][cos beta]12
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]10_______0_______15
c^2 = a^2 + b^2 - 2[a][b][cos beta]16
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]10_______0_______19
c^2 = a^2 + b^2 - 2[a][b][cos beta]20
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.6
c^2 = a^2 + b^2 - 2[a][b][cos beta]22
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
c^2 = a^2 + b^2 - 2[a][b][cos beta]24
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]6
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
alpha : 90 beta : 45 gamma : 458
c^2 = a^2 + b^2 - 2[a][b][cos beta]6_______0_______9
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
c^2 = a^2 + b^2 - 2[a][b][cos beta]31
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
alpha : 90 beta : 45 gamma : 458
c^2 = a^2 + b^2 - 2[a][b][cos beta]6_______0_______9
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
c^2 = a^2 + b^2 - 2[a][b][cos beta]37
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
alpha : 90 beta : 45 gamma : 458
c^2 = a^2 + b^2 - 2[a][b][cos beta]6_______0_______9
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
c^2 = a^2 + b^2 - 2[a][b][cos beta]43
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]45
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.4
c^2 = a^2 + b^2 - 2[a][b][cos beta]48
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.6
Java
c^2 = a^2 + b^2 - 2[a][b][cos beta]50
// of a triangle given coordinate
// of all three vertices
c^2 = a^2 + b^2 - 2[a][b][cos beta]53
c^2 = a^2 + b^2 - 2[a][b][cos beta]54
c^2 = a^2 + b^2 - 2[a][b][cos beta]53
c^2 = a^2 + b^2 - 2[a][b][cos beta]56
c^2 = a^2 + b^2 - 2[a][b][cos beta]57
c^2 = a^2 + b^2 - 2[a][b][cos beta]53
c^2 = a^2 + b^2 - 2[a][b][cos beta]56
c^2 = a^2 + b^2 - 2[a][b][cos beta]60
c^2 = a^2 + b^2 - 2[a][b][cos beta]53
c^2 = a^2 + b^2 - 2[a][b][cos beta]56
c^2 = a^2 + b^2 - 2[a][b][cos beta]63
c^2 = a^2 + b^2 - 2[a][b][cos beta]64
c^2 = a^2 + b^2 - 2[a][b][cos beta]65
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]6
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]5
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]56
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
c^2 = a^2 + b^2 - 2[a][b][cos beta]72
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]6
c^2 = a^2 + b^2 - 2[a][b][cos beta]75
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
c^2 = a^2 + b^2 - 2[a][b][cos beta]77
c^2 = a^2 + b^2 - 2[a][b][cos beta]75
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
c^2 = a^2 + b^2 - 2[a][b][cos beta]80
c^2 = a^2 + b^2 - 2[a][b][cos beta]75
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.4
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.5
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.6
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]56
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.7
c^2 = a^2 + b^2 - 2[a][b][cos beta]90
c^2 = a^2 + b^2 - 2[a][b][cos beta]91______0_______92
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]6
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
// Code to find all three angles
5beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
// Code to find all three angles
8beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
// of a triangle given coordinate
1beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]6
// of a triangle given coordinate
4beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
// of a triangle given coordinate
6beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
// of a triangle given coordinate
8 beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]11
// of a triangle given coordinate
8beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]13
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
// of a triangle given coordinate
8 beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]16
// of a triangle given coordinate
8beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]18
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
// of a triangle given coordinate
8 beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]21
// of a triangle given coordinate
8beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]23
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
#include
3beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
// of a triangle given coordinate
8 beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]29
// of a triangle given coordinate
8beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]31
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]32
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]33
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
// of a triangle given coordinate
8 beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]36
// of a triangle given coordinate
8beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]38
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]32
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]40
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
// of a triangle given coordinate
8 beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]43
// of a triangle given coordinate
8beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]45
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]32
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]47
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]00
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]29
// of a triangle given coordinate
8beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]54
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]55
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]56
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]36
// of a triangle given coordinate
8beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]60
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]55
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]56
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]43
// of a triangle given coordinate
8beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]66
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]55
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]56
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
c^2 = a^2 + b^2 - 2[a][b][cos beta]08
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]73_______0_______11
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]75
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]73_______5_______78
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]79
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]73_______0_______19
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]83
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.6
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]88
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]90
c^2 = a^2 + b^2 - 2[a][b][cos beta]56
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]93
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]6
c^2 = a^2 + b^2 - 2[a][b][cos beta]75
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]97
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]98
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]99
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.00
c^2 = a^2 + b^2 - 2[a][b][cos beta]9
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.00
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.03
c^2 = a^2 + b^2 - 2[a][b][cos beta]75
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.05
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]98
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]99
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.00
c^2 = a^2 + b^2 - 2[a][b][cos beta]9
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.10
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.03
c^2 = a^2 + b^2 - 2[a][b][cos beta]75
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.13_______5_______98
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]99
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.10
c^2 = a^2 + b^2 - 2[a][b][cos beta]9
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.00
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.03
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.20
c^2 = a^2 + b^2 - 2[a][b][cos beta]75
c^2 = a^2 + b^2 - 2[a][b][cos beta]45
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.6
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.6
Python3
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.26
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.27
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.28
c^2 = a^2 + b^2 - 2[a][b][cos beta]53
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.30
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.31
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.32
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.33
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.35
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.36
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.37
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.00
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.39
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.40
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.41
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.00
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.39
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.45_______16_______36
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.37
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.10
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.39
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.40
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.41
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.10
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.39
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.4
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.35
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.57
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.35
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.59
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.45
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.57
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.45
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.32
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.65
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.68
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.70
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.36
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.72
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.74
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.36
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.76
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.78
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.36
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.80
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.82
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.84
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.36
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.86
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.88
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.36
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.90
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.92
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.36
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.94
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.96
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.98
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.36
alpha : 90 beta : 45 gamma : 4500
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.59
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.78
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.40
alpha : 90 beta : 45 gamma : 4504
alpha : 90 beta : 45 gamma : 4505
alpha : 90 beta : 45 gamma : 4506
alpha : 90 beta : 45 gamma : 4507
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]32
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.57
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.88
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.57
alpha : 90 beta : 45 gamma : 4512
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
alpha : 90 beta : 45 gamma : 4514_______16_______36
alpha : 90 beta : 45 gamma : 4516
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.59
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.78
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.40
alpha : 90 beta : 45 gamma : 4520
alpha : 90 beta : 45 gamma : 4505
alpha : 90 beta : 45 gamma : 4506
alpha : 90 beta : 45 gamma : 4507
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]32
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.57
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.84
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.57
alpha : 90 beta : 45 gamma : 4512
beta = acos[ [ a^2 + b^2 - c^2 ] / [2ab] ]7
alpha : 90 beta : 45 gamma : 4530
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.36
alpha : 90 beta : 45 gamma : 4516
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.59
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.74
First, calculate the length of all the sides. Then apply above formula to get all angles in radian. Then convert angles from radian into degrees.40
alpha : 90 beta : 45 gamma : 4536
alpha : 90 beta : 45 gamma : 4505