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)

def solve(a, b, angle)
  ang = 1.0 * angle / 180 * Math::PI
  c = Math.sqrt(a ** 2 + b ** 2 - 2 * a * b * Math.cos(ang))
  area = 0.5 * a * b * Math.sin(ang)
  h = b * Math.sin(ang)
  [area, a + b + c, h]
end

def main
  a, b, ang = gets.split(/\s/).map(&:to_i)
  puts solve(a, b, ang)
end

main