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WAEC 2024 · Paper 1 · Q44

A cliff on the bank of a river is 87 m87\text{ m} high. A boat on the river is 22 m22\text{ m} away from the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff.

Worked solution (try it first)
  1. The angle of depression equals the angle of elevation of the cliff top from the boat (alternate angles).
  2. The height 87 m is opposite the angle and 22 m is adjacent: tan⁡θ=8722≈3.955\tan\theta = \frac{87}{22} \approx 3.955.
  3. So θ≈75.8∘\theta \approx 75.8^\circ, which is 76∘76^\circ to the nearest degree, option A.

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