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 final int A = 0;
	public static final int B = 1;
	
    public static void main( String args[] ) {
        Scanner scan = new Scanner( System.in );
		
		double a = scan.nextDouble();
		double b = scan.nextDouble();
		double C = scan.nextDouble();
		
		// S
		double S = a * b * Math.sin( Math.toRadians( C ) ) / 2;
		
		// L
		double L = a + b + Math.sqrt(a * a + b * b - 2 * a * b * Math.cos( Math.toRadians( C ) ) );
		
		// h
		double h = b * Math.sin( Math.toRadians( C ) );
		
		System.out.print(S + "\n" + L + "\n" + h + "\n");
		
	}
	
}