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.StdIn

object Main extends App {

  val Array(a, b, c) = StdIn.readLine().split(' ').map(_.toDouble)
  val rad = scala.math.toRadians(c)
  val s = (scala.math.sin(rad) * a * b ) / 2
  val h = scala.math.sin(rad) * b
  // 余弦定理
  val x = scala.math.sqrt(a*a + b*b - 2*b*a*scala.math.cos(rad)) + a + b
  
  println(f"$s%.8f")
  println(f"$x%.8f")
  println(f"$h%.8f")
  
}