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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.

  1. Sugar · Which side is missing?
    Student · The hypotenuse.
  2. Sugar · Square and add the legs.
    Student · 36 + 64 = 100.
  3. Sugar · Take the square root.
    Student · 10.

Answer: c = 10

Try 3 practice questions

  1. 1. Legs 5 and 12 — hypotenuse?

    Show answer

    13

  2. 2. Hypotenuse 10, one leg 6 — other leg?

    Show answer

    8

  3. 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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