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 final int BIG_NUM  = 2000000000;
    public static final int MOD  = 1000000007;
 
    public static void main(String[] args) {
 
        Scanner scanner = new Scanner(System.in);
        double a = scanner.nextDouble();
        double b = scanner.nextDouble();
        double degree = scanner.nextDouble();
 
        double S = 0.5*a*b*Math.sin(Math.PI*degree/180.0);
        double c = Math.sqrt(a*a+b*b-2*a*b*Math.cos(Math.PI*degree/180.0));
 
        System.out.printf("%.10f\n",S);
        System.out.printf("%.10f\n", a+b+c);
        System.out.printf("%.10f\n", 2*S/a);
    }
}