An observer 2 m tall is $24\sqrt{3} m$ away from a building. The angle of elevation of the top of the building as seen by him is 30°. What is the height of the building?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 26 m
The given distance is $24\sqrt{3}$ m.
Angle of elevation = $30^\circ$
$\tan 30^\circ = \frac{\text{Height of building} - \text{Height of observer}}{\text{Distance}}$
$\frac{1}{\sqrt{3}} = \frac{h - 2}{24\sqrt{3}}$
$h - 2 = 24$
$h = 26 \text{ m}$