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 Ruby (judge verdict: Accepted)

#!/usr/bin/env ruby

a, b, c = gets.chomp.split.map(&:to_f)

c_rad = c * Math::PI / 180

l = Math.sqrt(a**2 + b**2 - 2 * a * b * Math.cos(c_rad)) + a + b
h = b * Math.sin(c_rad)
s = a * h / 2

puts s, l, h