-- Gabe Schoenbach
-- Exercise 1.1

-- | 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

-- Exercise 1.4
-- | Change degrees into radians.

deg_to_rad :: Double -> Double
deg_to_rad d =  d * pi / 180

-- | Compute the length of one side of a triangle from the lengths of the other two sides a and b and gamma, the angle (in degrees) between a and b.

law_of_cosines :: Double -> Double -> Double -> Double
law_of_cosines a b gamma = sqrt (square a + square b - (2 * a * b * cos (deg_to_rad gamma)))