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 PHP (judge verdict: Accepted)

<?php

fscanf(STDIN, '%d %d %d', $a, $b, $C);

//三角関数で使えるように度をラジアンに変換する
$rad = deg2rad($C);

//面積を求める
$S = $a * $b / 2 * sin($rad);

//残りの１辺の長さを求める
$c = sqrt(pow($a, 2) + pow($b, 2) - 2 * $a * $b * cos($rad));

//3辺の合計
$L = $a + $b + $c;

//高さを求める
$h = $S / $a * 2;

printf("%f\n%f\n%f\n", $S, $L, $h);