Geometry and TrigonometryMediumHeight from a shadow ratio
Geometry and Trigonometry practice question
At the same moment, a vertical post 4 feet tall casts a shadow 6 feet long, and a nearby vertical flagpole casts a shadow 15 feet long. How tall is the flagpole, in feet?
Answer: 10
The sun's rays make similar triangles: height/shadow is the same for both. 4/6 = h/15, so h = 60/6 = 10.
Common wrong answers
- If you answered 6
- 6 is the post's shadow, not the flagpole's height.
- If you answered 13
- 13 adds the difference in shadows (9) to the post's height; the relationship is proportional, not additive.
- If you answered 22.5
- 22.5 comes from 6/4 = h/15, inverting the ratio.
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