Perimeter of Right Triangle by Tangents

Proposition: The perimeter of a right triangle equals the altitude to the hypotenuse multiplied by the sum of the Tan's of 1/2 the acute∠’s, divided by the product of the Tan's of 1/2 the acute ∠’s

You may say this is a non-problem, and you would be right. Simply add up the lengths of all 3 sides.

However, the proposition seeks to reveal just one of many mysterious and profound ways of mathematics.

To demonstrate, let the 8 15 17 Pythagorean triangle be our selection.