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)

/**
  * http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_10_B&lang=jp
  * Math Functions - Triangle
  */
object Main {
  def main(args: Array[String]): Unit = {
    val Array(a, b, degreeC) = io.StdIn.readLine().split(" ").map(_.toInt)
    val radianC = degreeC * math.Pi / 180.0
    val c = math.sqrt(a * a + b * b - 2.0 * a * b * math.cos(radianC))
    val el = a + b + c
    val s = el / 2.0
    val es = math.sqrt(s * (s - a) * (s - b) * (s - c))
    val h = 2.0 * es / a
    println(es)
    println(el)
    println(h)
  }
}