JAMB Mathematics 2023 Paper

The height of the second building H = h + 24

tan θ = $\frac{opp}{adj}$

tan 30$^{\circ} = \frac{h}{x}$

$\implies \frac{\sqrt{3}}{3} = \frac{h}{x}$

$\implies x = \sqrt{3} = 3h$

$\implies x = \frac{3h}{\sqrt{3}}$ ....(i)

tan 60$^{\circ} = \frac{24}{x}$

$\implies\sqrt{3} = \frac{24}{x}$

$\implies x\sqrt{3} = 24$

$\implies x = \frac{24}{\sqrt{3}}$ ....(ii)

Equate equation (i) and (ii)

$\implies \frac{3h}{\sqrt{3}} = \frac{24}{\sqrt{3}}$

$\implies$ 3h = 24

$\implies h = \frac{24}{3}$ = 8m

∴The height of the second building = 8 + 24 = 32m