给定二维平面中三角形所有三个顶点的坐标，任务是找到所有三个角。
例子：
Input : A = (0, 0),
B = (0, 1),
C = (1, 0)
Output : 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)
重新整理后
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）将三角形的边长与其中一个角的余弦联系起来。
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.
下面是上述步骤的实现。
C++
// Code to find all three angles
// of a triangle given coordinate
// of all three vertices
#include
#include // for pair
#include // for math functions
using namespace std;
#define PI 3.1415926535
// returns square of distance b/w two points
int lengthSquare(pair X, pair Y)
{
int xDiff = X.first - Y.first;
int yDiff = X.second - Y.second;
return xDiff*xDiff + yDiff*yDiff;
}
void printAngle(pair A, pair B,
pair C)
{
// Square of lengths be a2, b2, c2
int a2 = lengthSquare(B,C);
int b2 = lengthSquare(A,C);
int c2 = lengthSquare(A,B);
// length of sides be a, b, c
float a = sqrt(a2);
float b = sqrt(b2);
float c = sqrt(c2);
// From Cosine law
float alpha = acos((b2 + c2 - a2)/(2*b*c));
float betta = acos((a2 + c2 - b2)/(2*a*c));
float gamma = acos((a2 + b2 - c2)/(2*a*b));
// Converting to degree
alpha = alpha * 180 / PI;
betta = betta * 180 / PI;
gamma = gamma * 180 / PI;
// printing all the angles
cout << "alpha : " << alpha << endl;
cout << "betta : " << betta << endl;
cout << "gamma : " << gamma << endl;
}
// Driver code
int main()
{
pair A = make_pair(0,0);
pair B = make_pair(0,1);
pair C = make_pair(1,0);
printAngle(A,B,C);
return 0;
} Java
// Java Code to find all three angles
// of a triangle given coordinate
// of all three vertices
import java.awt.Point;
import static java.lang.Math.PI;
import static java.lang.Math.sqrt;
import static java.lang.Math.acos;
class Test
{
// returns square of distance b/w two points
static int lengthSquare(Point p1, Point p2)
{
int xDiff = p1.x- p2.x;
int yDiff = p1.y- p2.y;
return xDiff*xDiff + yDiff*yDiff;
}
static void printAngle(Point A, Point B,
Point C)
{
// Square of lengths be a2, b2, c2
int a2 = lengthSquare(B,C);
int b2 = lengthSquare(A,C);
int c2 = lengthSquare(A,B);
// length of sides be a, b, c
float a = (float)sqrt(a2);
float b = (float)sqrt(b2);
float c = (float)sqrt(c2);
// From Cosine law
float alpha = (float) acos((b2 + c2 - a2)/(2*b*c));
float betta = (float) acos((a2 + c2 - b2)/(2*a*c));
float gamma = (float) acos((a2 + b2 - c2)/(2*a*b));
// Converting to degree
alpha = (float) (alpha * 180 / PI);
betta = (float) (betta * 180 / PI);
gamma = (float) (gamma * 180 / PI);
// printing all the angles
System.out.println("alpha : " + alpha);
System.out.println("betta : " + betta);
System.out.println("gamma : " + gamma);
}
// Driver method
public static void main(String[] args)
{
Point A = new Point(0,0);
Point B = new Point(0,1);
Point C = new Point(1,0);
printAngle(A,B,C);
}
}Python3
# 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 ApurvaRajC#
// C# Code to find all three angles
// of a triangle given coordinate
// of all three vertices
using System;
class GFG
{
class Point
{
public int x, y;
public Point(int x, int y)
{
this.x = x;
this.y = y;
}
}
// returns square of distance b/w two points
static int lengthSquare(Point p1, Point p2)
{
int xDiff = p1.x - p2.x;
int yDiff = p1.y - p2.y;
return xDiff * xDiff + yDiff * yDiff;
}
static void printAngle(Point A, Point B, Point C)
{
// Square of lengths be a2, b2, c2
int a2 = lengthSquare(B, C);
int b2 = lengthSquare(A, C);
int c2 = lengthSquare(A, B);
// length of sides be a, b, c
float a = (float)Math.Sqrt(a2);
float b = (float)Math.Sqrt(b2);
float c = (float)Math.Sqrt(c2);
// From Cosine law
float alpha = (float) Math.Acos((b2 + c2 - a2) /
(2 * b * c));
float betta = (float) Math.Acos((a2 + c2 - b2) /
(2 * a * c));
float gamma = (float) Math.Acos((a2 + b2 - c2) /
(2 * a * b));
// Converting to degree
alpha = (float) (alpha * 180 / Math.PI);
betta = (float) (betta * 180 / Math.PI);
gamma = (float) (gamma * 180 / Math.PI);
// printing all the angles
Console.WriteLine("alpha : " + alpha);
Console.WriteLine("betta : " + betta);
Console.WriteLine("gamma : " + gamma);
}
// Driver Code
public static void Main(String[] args)
{
Point A = new Point(0, 0);
Point B = new Point(0, 1);
Point C = new Point(1, 0);
printAngle(A, B, C);
}
}
// This code is contributed by Rajput-Ji输出：
alpha : 90
betta : 45
gamma : 45
参考：
https://en.wikipedia.org/wiki/Law_of_cosines