Solve for hypotenuse or leg lengths in right triangles.
Overview
The Pythagorean theorem relates sides of a right triangle: a² + b² = c², where c is the hypotenuse opposite the right angle. It underlies distance in coordinate planes and vector magnitudes.
Given any two sides, solve for the third. For legs a,b and hypotenuse c, c = √(a²+b²) while a = √(c²−b²) when solving for a leg.
Always identify the hypotenuse as the longest side across from the right angle. Swapping legs does not matter, but treating a leg as hypotenuse inflates results.
Applications include construction squares, ladder safety reach, and GPS straight-line distance approximations on local scales.
Steps
Confirm the triangle is right.
Input two of a, b, c.
Solve for remaining side.
Square, sum or subtract, then square root.
Hypotenuse must exceed either leg.
Match precision to measurement context.
Math
a² + b² = c²
Square of hypotenuse equals sum of squares of legs in Euclidean geometry.
Worked cases
c = √(36+64) = √100
c = 10.
a = √(169−25) = √144
a = 12.
Diagonal = √(9+16)
5 units.
Why use this
Questions