A cliff overlooks the sea. From a point on the cliff, the angle of depression to a boat is $25^{\circ }$. If the horizontal distance of the boat from the base of the cliff is $200\text{m}$, find the height of the cliff.

Step-by-step solution

1. Recall that the angle of depression equals the angle of elevation from the boat to the point on the cliff.
2. Set up the right triangle with opposite side = height $h$ and adjacent side = $200\text{m}$.
3. Apply $\tan 25^{\circ }=\frac{h}{200}$, thus $h=200\tan 25^{\circ }$.
4. Use $\tan 25^{\circ }\approx 0.4663$ to obtain $h\approx 200\times 0.4663=93.26\text{m}$.
5. Round to one decimal place: $h\approx 93.3\text{m}$.

Concept tested: Height of cliff using angle of depression

Published 22 August 2026 · How this solution was prepared and checked

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