Question

What makes a triangle a “special” right triangle?
How can special right triangles help me find side lengths?

Answer 1

A special right triangle is a triangle with special features that can make calculations easier.
e.g.
the 30-60-90 triangle. If you know the shortest leg of this triangle (lets call it s), the longer leg is s*sqrt3, and the hypotenuse is 2s.

Answer 2

Likewise, the 45-45-90 triangle has two legs of equal length, and the hypotenuse is s*sqrt2