Home·Geometry

Missing Leg of a Right Triangle

Subtract the known leg squared from the hypotenuse squared and take the root. This is how you work out how far a leaning ladder’s base sits from the wall.

Your numbers

Side b

12cm

Angle (°)

22.62°

Formula

Side b = √(Hypotenuse² − Side a²)

The hypotenuse is always the longest side — entering a longer leg returns zero.

What to enter

InputDefaultAccepted range
Hypotenuse (cm)The longest side of a right triangle, facing the right angle.130 and up
Side a (cm)The length of the first side.50 and up

Step by step

FormulaSide b = √(Hypotenuse² − Side a²)
With the default numbersSide b = √(13² − 5²)
AnswerSide b = 12 cm

Quick reference table

Results when only Hypotenuse (cm) changes and everything else stays put.

Hypotenuse (cm)Side b (cm)Angle (°) (°)
6.54.153350.28
9.758.370330.85
131222.62
19.518.848114.86
2625.514711.09

What each result means

ResultAt default values
Side b (cm)The length of the second side.12
Angle (°) (°)An angle in degrees; a full turn is 360°.22.62

Common mistakes

The hypotenuse is always the longest side — entering a longer leg returns zero.

Glossary

Hypotenuse
The longest side of a right triangle, facing the right angle.
Side a
The length of the first side.
Side b
The length of the second side.
Angle (°)
An angle in degrees; a full turn is 360°.

Frequently asked questions

Q. How is Missing Leg of a Right Triangle calculated?

Side b = √(Hypotenuse² − Side a²) — Subtract the known leg squared from the hypotenuse squared and take the root. This is how you work out how far a leaning ladder’s base sits from the wall.

Q. Can you walk through an example?

With Hypotenuse 13cm, Side a 5cm, the answer is Side b 12cm.

Q. What do I need to enter?

Enter Hypotenuse, Side a. The result recalculates as you type, and an empty box counts as zero.

Q. How much does the answer move if I change a number?

Changing only Hypotenuse (cm) moves the answer to Hypotenuse (cm) 6.5 → Side b (cm) 4.1533 and Hypotenuse (cm) 26 → Side b (cm) 25.5147. The table below lays out five steps.

Q. How are the numbers rounded?

Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.

Q. Anything to watch out for?

The hypotenuse is always the longest side — entering a longer leg returns zero.

Related calculators

Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.