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 scan = new Scanner(System.in);
		int a = scan.nextInt();
		int b = scan.nextInt();
		int C = scan.nextInt();
		scan.close();
		double S = (a * b) / 2 * Math.sin(Math.toRadians(C));
		double c = Math.sqrt(a * a + b * b - (2 * a * b * Math.cos(Math.toRadians(C))));
		double L = a + b + c;
		double h = S * 2 / a;
		System.out.println(S);
		System.out.println(L);
		System.out.println(h);
	}
}