JAMB Mathematics 2012 Paper

Concept:Use the angle of depression to find the angle inside the right triangle, then apply tangent.Explanation:Let the distance of the boat from the base of the tree be $x$ cm.The tree is vertical, so the line from the base to the top is perpendicular to the ground.The angle of depression is $74^\circ$, so the angle between the line of sight and the vertical tree is:$$90^\circ - 74^\circ = 16^\circ$$Using the tangent ratio in the right triangle:$$\tan 16^\circ = \frac{x}{150}$$Thus:$$x = 150 \tan 16^\circ$$Evaluating gives:$$x \approx 43 \text{ cm}$$Answer:B. 43 cm