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 {
  def main(args: Array[String]): Unit = {
    val scanner = new java.util.Scanner(System.in)
    val a, b = scanner.nextDouble
    val ca = math.toRadians(scanner.nextDouble)

    val h = b * math.sin(ca)
    val s = a * h / 2
    val c = math.sqrt(a * a + b * b - 2 * a * b * math.cos(ca))
    println(f"$s%.5f")
    println(f"${a + b + c}%.5f")
    println(f"$h%.5f")
  }
}