WAEC Mathematics 2024 Paper

Concept:Use the tangent ratio in a right-angled triangle to find the angle of depression.Explanation:The angle of depression from the top of the cliff equals the angle of elevation from the boat, so both are $\alpha$.In the right-angled triangle formed, the height of the cliff is the side opposite $\alpha$, and the distance of the boat from the cliff is the side adjacent to $\alpha$.Using $\tan \alpha = \frac{\text{opposite}}{\text{adjacent}}$:$$\tan \alpha = \frac{87}{22}$$$$\tan \alpha = 3.9545$$$$\alpha = \tan^{-1}(3.9545)$$$$\alpha = 75.8^\circ$$Rounded to the nearest degree, $\alpha = 76^\circ$.Answer:A. $76^\circ$