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 Python3 (judge verdict: Accepted)

import math
if __name__ == '__main__':
    ans = input()
    a, b, C = ans.split()
    a, b, C = int(a), int(b), float(C)
    rad = math.radians(C)
    h = b * math.sin(rad)
    S = a * h / 2
    c = math.sqrt(a**2+b**2-2*a*b*math.cos(rad))
    L = a+b+c

    print(S)
    print(L)
    print(h)