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)

input = gets.split(" ")
a = input[0].to_f
b = input[1].to_f
c = input[2].to_f

s = (1.0/2.0)*a*b*Math.sin(c*Math::PI/180)
l = a + b + Math.sqrt( a**2 + b**2 - 2*a*b*Math.cos(c*Math::PI/180) )
h = b*Math.sin(c*Math::PI/180)

puts "%.8f" % s
puts "%.8f" % l
puts "%.8f" % h