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A lamp post stands on a horizontal plane. From a point situated at a distance $150 \mathrm{~m}$ from its foot, the angle of elevation of the top is $30^{\circ}$. What is the height of the lamp post ?
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The correct answer is:
$50 \sqrt{3} \mathrm{~m}$
In $\Delta \mathrm{ABC}$, we have $\mathrm{BC}=150 \mathrm{~m}, \mathrm{AB}=\mathrm{h}$
$\angle \mathrm{C}=30^{\circ}$
$\tan 30^{\circ}=\frac{\mathrm{h}}{150}$
$\Rightarrow \frac{1}{\sqrt{3}}=\frac{\mathrm{h}}{150}$
$\therefore \mathrm{h}=\frac{150}{\sqrt{3}} \mathrm{~m}$
$=\frac{150 \times \sqrt{3}}{3}=50 \sqrt{3} \mathrm{~m}$
$\angle \mathrm{C}=30^{\circ}$
$\tan 30^{\circ}=\frac{\mathrm{h}}{150}$
$\Rightarrow \frac{1}{\sqrt{3}}=\frac{\mathrm{h}}{150}$
$\therefore \mathrm{h}=\frac{150}{\sqrt{3}} \mathrm{~m}$
$=\frac{150 \times \sqrt{3}}{3}=50 \sqrt{3} \mathrm{~m}$
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