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 Scala (judge verdict: Accepted)

object Main extends App {
  val in = readLine.split(' ').map(_.toDouble)
  val a = in(0)
  val b = in(1)
  val C = in(2).toRadians

  val c = math.sqrt(a*a + b*b - 2*a*b*math.cos(C))

  val L = a + b + c;

  val h = b * math.sin(C)

  val S = a * h / 2;

  println(S)
  println(L)
  println(h)
}