A right triangle has hypotenuse 13 cm and one leg 5 cm. Find the other leg.
- b² = 13² − 5² = 169 − 25 = 144.
- A side length is positive, so b = √144.
Answer: 12 cm
Finding a Missing Leg Worksheets
Use a² + b² = c² for right triangles, coordinate distances and contextual problems.
Learn the skill
Finding a missing leg of a right triangle
For a right triangle, a² + b² = c², where c is the hypotenuse opposite the right angle. To find a missing leg, subtract the known leg’s square from the hypotenuse’s square, then take the positive square root.
A method you can use
- Confirm the triangle has a right angle and identify the hypotenuse.
- Write missing leg squared = hypotenuse squared − known leg squared.
- Take the positive square root and check that each leg is shorter than the hypotenuse.
Worked examples
The hypotenuse is 10 m and one leg is 6 m. Find the other leg.
- b² = 100 − 36 = 64.
- Take the positive square root.
Answer: 8 m
The hypotenuse is 7 cm and one leg is 3 cm. Give an exact missing length.
- b² = 49 − 9 = 40.
- √40 = √(4 × 10) = 2√10.
Answer: 2√10 cm
Try it yourself
Solve these before opening the answers. The printable sets below give you more practice.
1. A right triangle has hypotenuse 17 cm and one leg 8 cm. Find the other leg.
Show answer and explanation
15 cm
17² − 8² = 289 − 64 = 225; √225 = 15.
2. A right triangle has hypotenuse 5 m and one leg 3 m. Find the other leg.
Show answer and explanation
4 m
25 − 9 = 16; √16 = 4.
Before you begin
Read labeled dimensions and coordinates. Recall multiplication facts and length units.
Choose your level
- Easy: Use small whole-number measurements.
- Medium: Use larger dimensions or combine parts.
- Hard: Solve for a missing measure or explain a relationship.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
A right triangle has hypotenuse 10 cm and one leg 6 cm. Find the other leg.
2
A right triangle has hypotenuse 15 cm and one leg 9 cm. Find the other leg.
3
A right triangle has hypotenuse 20 cm and one leg 12 cm. Find the other leg.
4
A right triangle has hypotenuse 5 cm and one leg 3 cm. Find the other leg.
5
A right triangle has hypotenuse 25 cm and one leg 15 cm. Find the other leg.
6
A right triangle has hypotenuse 20 cm and one leg 12 cm. Find the other leg.
Answer Key
1. 8 cm2. 12 cm3. 16 cm4. 4 cm5. 20 cm6. 16 cm