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Finding the Height of a Flagpole Using a Mirror
publish date: 2026/05/14 21:51:47.679816 UTC
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To determine the height of a flagpole, a woman walks to a point 20 feet from its base, places a mirror on the ground, then steps back 2 feet farther — where she can see the top of the pole reflected in the mirror. Her eye level is 5 feet from the ground. Find the height \(h\) of the flagpole.
The two right triangles formed are similar. Set up and solve the proportion to find \(h\).
Correct Answer
50 ft
Explanation
The two triangles formed are similar (\(\triangle ABC \sim \triangle EDC\)). The proportion of corresponding sides gives:
\[\frac{h}{5} = \frac{20}{2}\]
Cross multiply: \(2h = 5 \times 20 = 100\) → \(h = 50\).
The flagpole is 50 feet tall.
Reference
Mathematics for college students