Home / How to find a missing leg

How to find a missing leg

Square the hypotenuse and the known leg, subtract, and take the square root. The hypotenuse must be longer than the known leg. If it is not, those two lengths do not belong to a right triangle.

Rearrange the theorem

The theorem says a² + b² = c². If c and b are known, then a² = c² − b², so a is the square root of that difference. Swap a and b if the other leg is the unknown one.

a = √(c² − b²)

b = √(c² − a²)

Steps

1. Identify the hypotenuse. It is opposite the right angle and must be the longest side.
2. Square the hypotenuse and square the known leg.
3. Subtract the smaller square from the larger one.
4. Take the square root. That is the missing leg.

Example

Hypotenuse 13 and leg 5: 169 − 25 = 144, and the square root of 144 is 12. The missing leg is 12. The triangle is 5-12-13.

Common mistakes

• Subtracting in the wrong order, which produces a negative number under the square root.
• Treating a leg as the hypotenuse. If your “hypotenuse” is shorter than the other given side, the labels are swapped or the triangle is not right.
• Using this method when you do not have a right angle. Check the three sides if you already know all of them.

How the app does it

Enter c and the known leg. Leave the other leg blank and calculate. The app rejects a hypotenuse that is not strictly longer than the known leg, and it rejects zero or negative lengths. Side lengths are entered as positive decimals; the angle field is the one that can be signed, and that belongs to Advanced mode.

If you know both legs instead, you are finding c, not a leg. Use the hypotenuse steps.

Get Pythagorean Theorem Calculator on Google Play

Related guides

Questions