Right Triangle Missing Leg Calculator

Formula

b = √(c² − a²)

Worked example

With Hypotenuse: 5 units, Known leg: 3 units, missing leg is 4 units.

Calculation method

The rule is b = √(c² − a²).

For this right triangle missing leg example, changing hypotenuse from 5 units to 6 units while keeping the other inputs fixed changes missing leg from 4 units to 5.196152 units.

Reading missing leg

A triangle’s area is half the corresponding base-times-height rectangle. In a right triangle, the hypotenuse is opposite the right angle and is the longest side. In the worked values on this page, hypotenuse 5 units, known leg 3 units produce missing leg 4 units.

Practical use

Use these formulas for surveying, drawings, roof geometry, and checking right-angle layouts. The specific task here is to find missing leg from hypotenuse, known leg.

Limits and common mistakes

The height must be perpendicular to the selected base. Three side lengths must satisfy the triangle inequality to form a real triangle. Verify hypotenuse in units before interpreting missing leg; a value measured on another basis would answer a different question.

Why the relationship works

The Pythagorean relationship applies only when the two legs meet at a right angle. Adding their squares gives the square of the hypotenuse; subtracting a known leg’s square from the hypotenuse squared recovers the other leg. This operation involves lengths, so take the appropriate square root at the end. The right triangle missing leg rule uses hypotenuse (units), known leg (units) in b = √(c² − a²); read each symbol as the field named on this page.

Interpreting another set of values

For right triangle missing leg, the fields labeled hypotenuse (units), known leg (units) are the known quantities. The calculator solves for missing leg in units using b = √(c² − a²). Label the actual base, perpendicular height, side lengths, or right-angle legs before using the answer. A result for area cannot be compared directly with a side length because their units differ. When comparing two calculations, keep their units and input definitions identical.

For a second right triangle missing leg check, keep the other default inputs fixed and change hypotenuse from 5 units to 7 units. Missing leg changes from 4 units to 6.324555 units. This is a comparison of two particular cases. Repeat it near the values relevant to your task; do not assume that every formula changes at a constant rate.

Checks and limits

The legs must meet at a right angle, and the hypotenuse must be longer than either leg. When finding a missing leg, a known leg longer than the hypotenuse cannot describe a right triangle. All lengths should use the same unit. The reported missing leg is 4 units in the worked example. Keep its stated unit or counting convention when checking it against another calculation.