1Cademy - Finding the Height of a Pole in a Right Triangle Display

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The Pythagorean Theorem

Example

Finding the Height of a Pole in a Right Triangle Display

Apply the seven-step problem-solving strategy and the Pythagorean Theorem to find an unknown side of a right triangle when two sides are equal.

Problem: Rene is setting up a holiday light display with two right triangles. The hypotenuse is $10$ feet, and the two legs are equal (the height of the pole and the distance to the stake). Find the height of the pole.

Read: A right triangle has a hypotenuse of $10$ and two equal legs.
Identify: The height of the pole.
Name: Let $x$ = the height of the pole. Then $x$ = the distance from the pole to the stake.
Translate: Write the Pythagorean Theorem and substitute: $a^2 + b^2 = c^2$ $x^2 + x^2 = 10^2$
Solve: Simplify to $2x^2 = 100$ . Divide by $2$ to get $x^2 = 50$ . Take the square root: $x = \pm\sqrt{50}$ . Simplify to $x = \pm5\sqrt{2}$ . Discard the negative solution because distance cannot be negative. Thus, $x = 5\sqrt{2} \approx 7.1$ .
Check: Verify the answer in the Pythagorean Theorem: $7.1^2 + 7.1^2 \approx 50.41 + 50.41 = 100.82$ , which is close to $10^2 = 100$ .
Answer: The pole should be about $7.1$ feet tall.

Updated 2026-05-25

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OpenStax Intermediate Algebra

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