JAMB Mathematics 2023 Paper

Concept:Use the tangent ratio for angles of elevation and depression to relate heights and horizontal distance.Explanation:Let the extra height of the second building above the first be $h$.Then the total height of the second building is $H = h + 24$. Let the horizontal distance between the two buildings be $x$.For the angle of elevation to the top:$\tan 30^\circ = \frac{h}{x}$$\frac{\sqrt{3}}{3} = \frac{h}{x}$$x = \frac{3h}{\sqrt{3}}$ ... (i)For the angle of depression to the bottom:$\tan 60^\circ = \frac{24}{x}$$\sqrt{3} = \frac{24}{x}$$x = \frac{24}{\sqrt{3}}$ ... (ii)Equate equations (i) and (ii):$\frac{3h}{\sqrt{3}} = \frac{24}{\sqrt{3}}$$3h = 24$$h = 8$ mTherefore, the height of the second building is:$H = h + 24 = 8 + 24 = 32$ mAnswer:$32$ mOption D.