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;
using System.Linq;

namespace myApp
{
    class Program
    {
        static void Main(string[] args)
        {
            var line = Console.ReadLine().Split(' ');
            var a = int.Parse(line[0]);
            var b = int.Parse(line[1]);
            var c = int.Parse(line[2]);

            // 面積を求める
            // 1/2absinθ
            double S = a * b * Math.Sin(c * Math.PI / 180) / 2d;
            Console.WriteLine(S.ToString());

            // 周の長さ
            // L = a + b + √a*a + b*b - 2abcosθ
            double L = a + b + Math.Sqrt(a * a + b * b - 2d * a * b * Math.Cos(c * Math.PI / 180));
            Console.WriteLine(L.ToString());

            // aを底辺としたときの高さh
            // h = bsinθ
            double h = b * Math.Sin(c * Math.PI / 180);
            Console.WriteLine(h.ToString());
        }
    }
}