Math Geometry • Basic Shapes and Properties
Solve right-triangle sides using \(a^2 + b^2 = c^2\) — compute the hypotenuse, find a missing leg, or verify whether three sides form a right triangle.
Tip: In “Solve” modes, the computed side is locked (you can’t type into it). In “Verify”, all three sides are editable.
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For a right triangle with legs a and b, the hypotenuse is c = sqrt(a^2 + b^2). Enter a and b to compute c.
Rearrange a^2 + b^2 = c^2 to isolate the missing leg: a = sqrt(c^2 - b^2) or b = sqrt(c^2 - a^2). The hypotenuse c must be larger than either leg.
Treat the largest side as c and test whether a^2 + b^2 equals c^2. Small differences can occur due to rounding, so calculators often use a tolerance.
The hypotenuse is the longest side and it lies opposite the 90-degree angle. In the Pythagorean theorem it is labeled c.
Because c is the hypotenuse, it must be the longest side of a right triangle. If c is not larger than the known leg, c^2 - leg^2 becomes zero or negative and no valid real leg length exists.