Using the Pythagorean theorem
a² + b² = c², where c is always the side opposite the right angle.
The common mistake
Treating any side as c — adding squares when the missing side is a leg.
Instead: Identify the hypotenuse first. Missing hypotenuse: add squares. Missing leg: subtract from c².
Worked example with Guide me
A right triangle has legs 6 and 8. Find the hypotenuse.
- Sugar · Which side is missing?Student · The hypotenuse.
- Sugar · Square and add the legs.Student · 36 + 64 = 100.
- Sugar · Take the square root.Student · 10.
Answer: c = 10
Try 3 practice questions
1. Legs 5 and 12 — hypotenuse?
Show answer
13
2. Hypotenuse 10, one leg 6 — other leg?
Show answer
8
3. Legs 1 and 1 — hypotenuse?
Show answer
√2 ≈ 1.41
Quick answers
- What is the most common mistake with using the pythagorean theorem?
- Treating any side as c — adding squares when the missing side is a leg.
- How do I get using the pythagorean theorem right?
- Identify the hypotenuse first. Missing hypotenuse: add squares. Missing leg: subtract from c².
- Can you show a worked example?
- A right triangle has legs 6 and 8. Find the hypotenuse. c = 10
Related concepts
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