Triangle areas

-- 3 methods of getting the area of a triangle
areaOfTriangleHeron a b c = sqrt (s*(s-a)*(s-b)*(s-c)) -- calculate area of a triangle from the length of it's three sides using heron's fomula
    where
    s = (a+b+c) / 2

areaOfTriangleTrigUnopt a b c = c * height / 2 -- calculate the area of a triangle with modern trigonometry
    where
    cosa = (b^2 + c^2 - a^2) / (2*b*c)
    sina = sqrt (1 - cosa^2)
    height = b*sina


areaOfTriangleTrig a b c = 0.5 * a * b * sin c -- optimized triangles with trigonometry