Python 找出给定三角形的所有角度（Find all angles of a given triangle）

本文链接：https://blog.youkuaiyun.com/hefeng_aspnet/article/details/144345595

给定三角形在二维平面上所有三个顶点的坐标，任务是找到所有三个角度。
示例：

输入：A = (0, 0),
B = (0, 1),
C = (1, 0)
输出：90, 45, 45

为了解决这个问题，我们使用下面的余弦定律。

c^2 = a^2 + b^2 - 2(a)(b)(cos beta)

重新安排后

beta = acos( ( a^2 + b^2 - c^2 ) / (2ab) )

在三角学中，余弦定律（也称为余弦公式或余弦规则）将三角形边的长度与其某个角的余弦联系起来。

首先，计算所有边的长度。然后应用上述公式得到所有角度的弧度。然后将角度从弧度转换为度数。

以下是上述步骤的实施：

# Python3 code to find all three angles
# of a triangle given coordinate
# of all three vertices
import math

# returns square of distance b/w two points
def lengthSquare(X, Y):
xDiff = X[0] - Y[0]
yDiff = X[1] - Y[1]
return xDiff * xDiff + yDiff * yDiff

def printAngle(A, B, C):

# Square of lengths be a2, b2, c2
a2 = lengthSquare(B, C)
b2 = lengthSquare(A, C)
c2 = lengthSquare(A, B)

# length of sides be a, b, c
a = math.sqrt(a2);
b = math.sqrt(b2);
c = math.sqrt(c2);

# From Cosine law
alpha = math.acos((b2 + c2 - a2) /
(2 * b * c));
betta = math.acos((a2 + c2 - b2) /
(2 * a * c));
gamma = math.acos((a2 + b2 - c2) /
(2 * a * b));

# Converting to degree
alpha = alpha * 180 / math.pi;
betta = betta * 180 / math.pi;
gamma = gamma * 180 / math.pi;

# printing all the angles
print("alpha : %f" %(alpha))
print("betta : %f" %(betta))
print("gamma : %f" %(gamma))

# Driver code
A = (0, 0)
B = (0, 1)
C = (1, 0)

printAngle(A, B, C);

# This code is contributed
# by ApurvaRaj