2D 平面内の三角形の 3 つの頂点すべての座標が与えられた場合、タスクは 3 つの角度すべてを見つけることです。
例:
Input : A = (0 0) B = (0 1) C = (1 0) Output : 90 45 45
この問題を解決するには、以下を使用します 余弦の法則 。

ウェブブラウザの設定
scan.next Java
c^2 = a^2 + b^2 - 2(a)(b)(cos beta)
整理し直してから
beta = acos( ( a^2 + b^2 - c^2 ) / (2ab) )
三角法では、余弦の法則 (余弦公式または余弦定理とも呼ばれます) は、三角形の辺の長さをその角度の 1 つの余弦に関連付けます。
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.
以下は上記の手順の実装です。
// 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<intint> X pair<intint> Y) { int xDiff = X.first - Y.first; int yDiff = X.second - Y.second; return xDiff*xDiff + yDiff*yDiff; } void printAngle(pair<intint> A pair<intint> B pair<intint> C) { // Square of lengths be a2 b2 c2 int a2 = lengthSquare(BC); int b2 = lengthSquare(AC); int c2 = lengthSquare(AB); // 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 beta = acos((a2 + c2 - b2)/(2*a*c)); float gamma = acos((a2 + b2 - c2)/(2*a*b)); // Converting to degree alpha = alpha * 180 / PI; beta = beta * 180 / PI; gamma = gamma * 180 / PI; // printing all the angles cout << 'alpha : ' << alpha << endl; cout << 'beta : ' << beta << endl; cout << 'gamma : ' << gamma << endl; } // Driver code int main() { pair<intint> A = make_pair(00); pair<intint> B = make_pair(01); pair<intint> C = make_pair(10); printAngle(ABC); 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(BC); int b2 = lengthSquare(AC); int c2 = lengthSquare(AB); // 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(00); Point B = new Point(01); Point C = new Point(10); printAngle(ABC); } }
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
JavaScript // JavaScript program // Code to find all three angles // of a triangle given coordinate // of all three vertices // returns square of distance b/w two points function lengthSquare(X Y){ let xDiff = X[0] - Y[0]; let yDiff = X[1] - Y[1]; return xDiff*xDiff + yDiff*yDiff; } function printAngle(A B C){ // Square of lengths be a2 b2 c2 let a2 = lengthSquare(BC); let b2 = lengthSquare(AC); let c2 = lengthSquare(AB); // length of sides be a b c let a = Math.sqrt(a2); let b = Math.sqrt(b2); let c = Math.sqrt(c2); // From Cosine law let alpha = Math.acos((b2 + c2 - a2)/(2*b*c)); let beta = Math.acos((a2 + c2 - b2)/(2*a*c)); let gamma = Math.acos((a2 + b2 - c2)/(2*a*b)); // Converting to degree alpha = alpha * 180 / Math.PI; beta = beta * 180 / Math.PI; gamma = gamma * 180 / Math.PI; // printing all the angles console.log('alpha : ' alpha); console.log('beta : ' beta); console.log('gamma : ' gamma); } // Driver code let A = [0 0]; let B = [0 1]; let C = [1 0]; printAngle(ABC); // The code is contributed by Gautam goel (guatamgoel962)
出力:
alpha : 90 beta : 45 gamma : 45
時間計算量: 組み込みの sqrt 関数を使用しているため、O(log(n))
補助スペース: ○(1)
jvm
参照 :
https://en.wikipedia.org/wiki/余弦の法則