A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist.
Angle based right triangle: 30-60-90, 45-45-90. (Angles that form a simple ratio)
Side based right triangle: 3-4-5 (The lengths of the sides form a whole number ratio),
approx angles 37-53.
Knowing the ratios of the angles or sides of these special right triangles allows one to quickly calculate various lengths in geometric problems without resorting to more advanced methods.