③ Why this works

A right triangle is fully determined by two pieces of information because the 90° angle plus the angle sum (180°) leaves the acute angles complementary (A + B = 90°). Combine that with the Pythagorean theorem (a² + b² = c²) and the SOH-CAH-TOA trig ratios (sin A = a/c, cos A = b/c, tan A = a/b), and every unknown follows.