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.io.Source
import scala.math.{ sin, cos, sqrt, Pi }

object Main extends App {
  val Array(bottom: Double, slope: Double, angle: Double) = Source.stdin.getLines.next.split(" ").map(_.toDouble)

  def toRadians(angle: Double) = {
    angle * (math.Pi / 180)
  }

  val h = sin(toRadians(angle)) * slope
  val area = bottom * h / 2
  val length = bottom + slope + sqrt(bottom * bottom + slope * slope - 2 * bottom * slope * cos(Pi * angle / 180))

  println(area)
  println(length)
  println(h)
}