# Find all angles of a given triangle

Given coordinates of all three vertices of the triangle in the 2D plane, the task is to find all three angles.

Example:

```Input : A = (0, 0),
B = (0, 1),
C = (1, 0)
Output : 90, 45, 45
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

To solve this problem we use below Law of cosines. ```c^2 = a^2 + b^2 - 2(a)(b)(cos beta)
```

After re-arranging

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

In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.

```First, calculate the length of all the sides.
Then apply above formula to get all angles in
degrees.
```

Below is implementation of above steps.

## 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<``int``,``int``> X, pair<``int``,``int``> Y) ` `{ ` `    ``int` `xDiff = X.first - Y.first; ` `    ``int` `yDiff = X.second - Y.second; ` `    ``return` `xDiff*xDiff + yDiff*yDiff; ` `} ` ` `  `void` `printAngle(pair<``int``,``int``> A, pair<``int``,``int``> B, ` `                ``pair<``int``,``int``> 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<``int``,``int``> A = make_pair(0,0); ` `    ``pair<``int``,``int``> B = make_pair(0,1); ` `    ``pair<``int``,``int``> 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 ApurvaRaj `

## C#

 `// 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 `

Output:

```alpha : 90
betta : 45
gamma : 45
```

This article is contributed by Pratik Chhajer . If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up

Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.