Haskell triangle calculation

triangle.hs

data Side = Adjacent Double | Opposite Double | Hypotenuse Double deriving Show 

type Angles = Maybe (Double, Double, Double)

type Sides = Maybe (Double, Double, Double)

data Triangle = Triangle Angles Sides

toDegrees :: Double -> Double
toDegrees rad = rad * 360 / (2 * pi)

toRadian :: Double -> Double
toRadian deg = deg * 2 * pi / 360  

instance Show Triangle where
    show (Triangle (Just (a1, a2, a3)) (Just (s1, s2, s3))) = 
        "Angles: "  
            ++ show (round $ toDegrees a1) 
            ++ ", " ++ show (round $ toDegrees a2) 
            ++ ", " ++ show (round $ toDegrees a3)
        ++ "\nSides: "
            ++ show s1
            ++ ", " ++ show s2
            ++ ", " ++ show s3

calcTriangle :: Double -> Side -> Triangle
calcTriangle angle side = loop $ Triangle Nothing Nothing
    where 
        a1 = toRadian angle
        loop triangle = case triangle of
            (Triangle _ sides@(Just (adj, op, hyp))) ->
                let a2 = acos (op / hyp) in  
                Triangle (Just (a1, a2, pi - a1 - a2)) sides
            (Triangle _ _) -> case side of
                (Adjacent side) ->
                    loop . Triangle Nothing $ Just (side, tan a1 * side, side / cos a1) 
                (Opposite side) ->
                    loop . Triangle Nothing $ Just (side / tan a1, side, side / sin a1) 
                (Hypotenuse side) ->
                    loop . Triangle Nothing $ Just (cos a1 * side, sin a1 * side, side)
                    
{-
*Main> putStrLn . show $ calcTriangle 60 (Hypotenuse 2) 
Angles: 60, 30, 90
Sides: 1.0000000000000002, 1.7320508075688772, 2.0
-}