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
list = input().split()
a = float(list[0])
b = float(list[1])
C = float(list[2])

C = math.radians(C)

S = a * b * math.sin(C) / 2
c = math.sqrt(a ** 2 + b ** 2 - 2 * a * b * math.cos(C))
L = a + b + c
h = 2 * S / a

print("{:.5f}".format(S))
print("{:.5f}".format(L))
print("{:.5f}".format(h))