WAEC Mathematics 2023 Paper

Concept:In a right-angled triangle, $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$.Here, the height of the building is the opposite side and the required distance is the adjacent side.Explanation:Let the distance from $Z$ to the foot of the building be $d$ metres.Given: angle of elevation $= 50^\circ$, height $= 124$ m.Using the tangent ratio:$$\tan 50^\circ = \frac{124}{d}$$Rearrange to find $d$:$$d = \frac{124}{\tan 50^\circ}$$Using $\tan 50^\circ \approx 1.1918$,$$d = \frac{124}{1.1918} \approx 104.05 \text{ m}$$Answer:The distance from $Z$ to the foot of the building is $104.05$ m.Correct option: B. $104.05$ m.