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    <p>Seeing <code>Floating a</code> and <code>Integral a</code> in a type signature together always sets off my internal alarm bells, as these classes are supposed to be mutually exclusive - at least, there are no standard numeric types that are instances of both classes. GHCi tells me (along with a lot of other stuff):</p> <pre><code>&gt; :info Integral ... instance Integral Integer -- Defined in `GHC.Real' instance Integral Int -- Defined in `GHC.Real' &gt; :info Floating ... instance Floating Float -- Defined in `GHC.Float' instance Floating Double -- Defined in `GHC.Float' </code></pre> <p>To see why these classes are mutually exclusive, let's have a look at some of the methods in both classes (this is going to be a bit handwavy). <code>fromInteger</code> in <code>Integral</code> converts an <code>Integral</code> number to an <code>Integer</code>, without loss of precision. In a way, <code>Integral</code> captures the essence of being (a subset of) the mathematical integers.</p> <p>On the other hand, <code>Floating</code> contains methods such as <code>pi</code> and <code>exp</code>, which have a pronounced 'real number' flavour. </p> <p>If there were a type that was both <code>Floating</code> and <code>Integral</code>, you could write <code>toInteger pi</code> and have a integer that was equal to 3.14159... - and that's not possible :-)</p> <hr> <p>That said, you should change all your type signatures to use <code>Double</code> instead of <code>Int</code>; after all, not all triangles have integer sides, or angles that are an integral number of degrees!</p> <p>If you <em>absolutely</em> don't want that for whatever reason, you also need to convert the sides (the <code>a</code> and <code>b</code> arguments) in <code>lawOfCosines</code> to <code>Double</code>. That's possible via</p> <pre><code>lawOfCosines aInt bInt gamma = sqrt $ a*a + b*b - 2*a*b*(cos (toRadians gamma)) where a = fromInteger aInt b = fromInteger bInt </code></pre>
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    1. COIn fact, one might say that, under any reasonable measure, _almost all_ triangles do not have integer sides. (Though the same applies for rational / double, but those at least approximate ℝ properly.)
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