-- Zhang Xiaomenghan
-- Exercise 1.4

-- | A module for working with triangles.

module Hypotenuse where

-- | Compute the length of the hypotenuse of a triangle from the lengths
--   of its sides.
hypotenuse :: Double -> Double -> Double
hypotenuse a b = sqrt (square a + square b)

-- | Square a number.
square :: Num n => n -> n
square x = x ^ 2

-- | Law of cosine
law_of_cosines :: Double -> Double -> Double -> Double
law_of_cosines a b gamma = sqrt $ a^2 + b^2 - 2 * a * b * cos (gamma/180 * pi)



SAMPLE RUNS IN GHCI:

*Hypotenuse> law_of_cosines 4 5 6
1.1041395678396217
Hypotenuse> law_of_cosines 1 1 60
0.9999999999999999
*Hypotenuse> law_of_cosines 4 4 90
5.65685424949238
*Hypotenuse> law_of_cosines 3 4 90
5.0
*Hypotenuse> law_of_cosines 3 6 25
3.5175161217371276