Discussion
Due to sun, a 6ft man casts a shadow of 4ft, whereas a pole next to the man casts a shadow of 36ft. What is the height of the pole?
Answer: C
The sun's rays hit the man and the pole at the same angle, so the two object–shadow triangles are similar and the ratio of height to shadow is the same for both.
\[ \frac{\text{man's height}}{\text{man's shadow}} = \frac{\text{pole's height}}{\text{pole's shadow}} \]
\[ \frac{6}{4} = \frac{h}{36} \]
\[ h = 36 \times \frac{6}{4} = 36 \times 1.5 = 54 \text{ ft} \]
The same result by scale factor: the pole's shadow is \( 36 \div 4 = 9 \) times the man's, so the pole is 9 times his height, \( 9 \times 6 = 54 \) ft. Multiplying 6 by 6 instead treats the shadow ratio as \( 36 \div 6 \), which mixes a height with a length.
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