Problem:
Triangle

For given two sides of a triangle a and b and the angle C between them, calculate the following properties:

S: Area of the triangle

L: The length of the circumference of the triangle

h: The height of the triangle with side a as a bottom edge

Input

The length of a, the length of b and the angle C are given in integers.

Output

Print S, L and h in a line respectively. The output should not contain an absolute error greater than 10-4.

Sample Input

4 3 90

Sample Output

6.00000000
12.00000000
3.00000000

Solution in JAVA (judge verdict: Accepted)

import java.util.*;

public class Main {
    
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        double a = sc.nextDouble();
        double b = sc.nextDouble();
        double c = sc.nextDouble()*(Math.PI/180);
        
        double s =(a*b*Math.sin(c))/2;
        double l = Math.sqrt(a*a + b*b -2*a*b*Math.cos(c))+a+b;
        double h = (2*s)/a;
        
        System.out.printf("%f\n%f\n%f\n",s,l,h);
    }
}