A street light is fixed at the top of a pole. From a point on the ground 30 m away from the pole, the angle of elevation of the light is $35^{\circ }$. A man 1.8 m tall stands between the pole and the point, casting a shadow of length 8 m on the ground. Find the height of the pole.

Step-by-step solution

1. Let the pole be at $P$, the man at $M$, and the observation point at $O$.
2. The total distance $PO=30\text{m}$.
3. The man's shadow length is 8 m, so $MO=8\text{m}$.
4. Therefore the distance from the pole to the man is $PM=PO-MO=30-8=22\text{m}$.
5. From point $O$, $\tan 35^{\circ }=\frac{\text{height of pole }(H)}{30}$ (because $OP$ is the adjacent side).
6. Hence $H=30\tan 35^{\circ }$.
7. Using $\tan 35^{\circ }\approx 0.7002$, calculate $H\approx 30\times 0.7002=21.01\text{m}$.
8. Rounded to one decimal place, the pole is $21.0\text{m}$ tall.

Concept tested: Height from angle of elevation with extra data

Published 20 August 2026 · How this solution was prepared and checked