Vice versa , when a half - angle tangent is a rational number in the interval ( 0 , 1 ) , there is a right triangle that has the full angle .
That has side lengths that are a Pythagorean triple .
Vice versa , when a half - angle tangent is a rational number in the interval ( 0 , 1 ) , there is a right triangle that has the full angle and that has side lengths that are a Pythagorean triple .