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All courses Geometry · G-SRT.8 38 of 57
Use trig ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Find the missing side of a right triangle by identifying the legs and hypotenuse

Problem
Use the \(\text{Pythagorean}~\text{Theorem}\) to find the missing side: legs \(6\) and \(8\)
Your answer
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Hint

Since both legs are given, use \(a^2+b^2=c^2\) to find the hypotenuse.

In a right triangle, the hypotenuse squared equals the sum of the squares of the legs.

Solution walkthrough

01

Identify the right-triangle parts

\[\text{legs}=6~\text{and}~8;~\text{hypotenuse}=c\]

The Pythagorean theorem applies because the two supplied lengths are perpendicular legs and the unknown is the hypotenuse.

02

Substitute

\[6^2+8^2=c^2\]

The squared leg lengths add to the squared hypotenuse.

03

Evaluate and solve

\[36+64=100=c^2~->~c=\sqrt{100}=10\]

A geometric length uses the positive square root.

04

Check

\[6^2+8^2=10^2~\text{and}~10>8\]

The equation balances, and the hypotenuse is longer than either leg.

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Another way

  1. Recognize 6-8-10 as twice the 3-4-5 right-triangle triple.

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Common mistake

Do not stop at c squared equals 100. Take the positive square root to obtain the length 10.

Solution walkthrough video