Ease of Calculation
Rational trigonometry makes some problems solvable with only addition, subtraction, multiplication, and division, with fewer uses of other functions such as square roots, sine, and cosine compared to classical trigonometry. Such algorithms execute more efficiently on most computers, for problems such as solving triangles. Other computations, however, do involve more computations than their classical analogues; such computations include determining the quadrance of a line segment given the quadrance of two collinear line segments which compose it, or such as computing the spread of the sum of two angles with known spreads.
Read more about this topic: Rational Trigonometry
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—Henri-Frédéric Amiel (1821–1881)