From a point on level ground 40 m away from the base of a lighthouse, the angle of elevation of the top is $22^{\circ }$. Find the height of the lighthouse correct to two decimal places.

Step-by-step solution

1. In a right‑angled triangle, $\tan \theta =\frac{\text{opposite}}{\text{adjacent}}$. Here, opposite = height $h$, adjacent = 40 m, $\theta =22^{\circ }$.
2. Write $\tan 22^{\circ }=\frac{h}{40}$.
3. Hence $h=40\tan 22^{\circ }$.
4. Using $\tan 22^{\circ }\approx 0.4040$, compute $h\approx 40\times 0.4040=16.160$.
5. Round to two decimal places: $h=16.16\text{ m}$.

Concept tested: Angle of elevation using tangent

Published 25 August 2026 · How this solution was prepared and checked

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