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)

import scala.math._

object Main extends App {
  val scanner = new java.util.Scanner(System.in)

  val a = scanner.nextInt()
  val b = scanner.nextInt()
  val C = scanner.nextInt()
  val c = C / 360.0 * 2 * Pi
  
  val S = b * (a * sin(c)) / 2
  val L = a + b + sqrt(a*a + b*b - 2*a*b*cos(c))
  val h = b * sin(c)

  val outputs = Seq(S, L, h)

  outputs.foreach(println)
}