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.Scanner;

public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        double a = sc.nextDouble(), b = sc.nextDouble(), angle = sc.nextDouble();
        double c = Math.toRadians(angle);
        
        double s = a * b * Math.sin(c) / 2;
        double l = a + b + Math.sqrt(a * a + b * b - 2 * a * b * Math.cos(c));
        double h = b * Math.sin(c);
        
        System.out.println(s);
        System.out.println(l);
        System.out.println(h);
    }
}