Solving Right Triangles

Any two values of a right triangle determine the rest. Given two legs, the hypotenuse follows from Pythagoras; given a leg and the hypotenuse, the other leg follows by rearrangement. Angles come from the arcsin of side ratios, and area is half the product of the legs.

Trigonometry Connections

In a right triangle, sin A = opposite ÷ hypotenuse, cos A = adjacent ÷ hypotenuse, and tan A = opposite ÷ adjacent. These ratios are the foundation of surveying, navigation, and physics — every vector decomposition is a right triangle.

Real-World Applications

Ramps must meet specific rise-to-run ratios, roofs need pitch angles, and screen sizes use the diagonal. Construction workers square corners with the 3-4-5 method — the fastest real-world use of the theorem.