A man 2 m tall is walking away from a street light of height 10 m. If the length of his shadow is 6 m, find the distance of the man from the street light.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 24 m
The light ray from the top of the street light passes over the man’s head to the tip of his shadow. The street light and the man both stand upright on the ground, so the two right-angled triangles they form with this ray are similar, and their sides are in the same ratio.
Large triangle: height 10 m, base \(d+6\) m; small triangle: height 2 m, base 6 m
Corresponding sides are in the same ratio: \(\displaystyle\frac{10}{2}=\frac{d+6}{6}\)
So \(d+6=30\), and the man is \(d=\) 24 m from the street light