An Exact Angle

The special values run backwards too. If a ratio comes out as the entry in its own function's column of the table, the acute angle is exact: no calculator, no rounding.

A right triangle has legs of 3 and 3√(3). For the angle θ opposite the longer leg, tan(theta) = (3√(3))/3, which is √3. The table says tan 60° = √3, so θ is exactly 60°. A ratio like 5/8, which is not in the table, gives an angle that has to be rounded.