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.io.BufferedReader;
import java.io.InputStreamReader;
import java.lang.Math.*;
import java.util.*;
import java.math.*;
import java.text.*;
public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        double a = sc.nextDouble();
        double b = sc.nextDouble();
        double c = sc.nextDouble();
        NumberFormat nf = NumberFormat.getInstance();
        nf.setMaximumFractionDigits(8);
        nf.setGroupingUsed(false);
        //aのほうが大きい
        //S=1/2ab sin0;
        //h = bsin0
        //L = a + b + √a^2+b^2-2abcosθ 
        System.out.println(nf.format(1*a*b*Math.sin(Math.toRadians(c)) / 2));
        System.out.println(nf.format(a + b + Math.sqrt(Math.pow(a,2) + Math.pow(b,2) - 2 * a * b * Math.cos(Math.toRadians(c)))));
        System.out.println(nf.format(b * Math.sin(Math.toRadians(c))));
    }
}