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 C# (judge verdict: Accepted)

using System;

public class ITP1_10_B{
    public static void Main(){
        var items = Console.ReadLine().Split(' ');
        
        var a = double.Parse(items[0]);
        var b = double.Parse(items[1]);
        var C = double.Parse(items[2]);
        
        var C_rad = C / 180 * Math.PI;
        
        var S = a * b * Math.Sin(C_rad) / 2;
        
        var c = Math.Sqrt(a * a + b * b - 2 * a * b * Math.Cos(C_rad));
        var L = a + b + c;
        
        var h = 2 * S / a;
        
        Console.WriteLine(S);
        Console.WriteLine(L);
        Console.WriteLine(h);
    }
}