Geometry and TrigonometryHardHeights from shadows
Geometry and Trigonometry practice question
At the same moment, a person 1.8 metres tall casts a shadow 2.4 metres long, and a nearby tree casts a shadow 12 metres long. What is the height of the tree, in metres?
Answer: 9
The sun's rays make similar right triangles, so height/shadow is the same for both: 1.8/2.4 = h/12. Then h = 12 × 1.8/2.4 = 12 × 0.75 = 9.
Common wrong answers
- If you answered 16
- 16 is 12 × 2.4/1.8, the ratio upside down. Height is 0.75 times shadow length here, so the tree is shorter than its shadow.
- If you answered 11.4
- 11.4 is 12 − 0.6, subtracting the person's shadow-minus-height difference. The relationship is a ratio, not a fixed difference.
- If you answered 10.8
- 10.8 is 12 × 0.9; the ratio is 1.8/2.4 = 0.75.
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