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 scanner = new Scanner(System.in);

        double a = scanner.nextDouble();
        double b = scanner.nextDouble();
        double c = scanner.nextDouble();

        double area = a * b * Math.sin(Math.toRadians(c)) / 2;
        double h = b * Math.sin(Math.toRadians(c));
        double d = Math.sqrt(a*a + b * b - 2 * a * b * Math.cos(Math.toRadians(c)));

        System.out.println(area + " " + (d + a + b) + " " + h);
        scanner.close();
    }
}