The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is 30° than when it is 60°. Find the height of the tower.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $20\sqrt{3} m$
Let the height of the tower be h m.
Shadow length $= h \cot \theta$
- At $30^\circ$: shadow $= h \cot 30^\circ = h\sqrt{3}$
- At $60^\circ$: shadow $= h \cot 60^\circ = \frac{h}{\sqrt{3}}$
Given difference in shadows = 40 m:
$h\left(\sqrt{3} - \frac{1}{\sqrt{3}}\right) = 40$
$h \cdot \frac{2}{\sqrt{3}} = 40$
$h = \frac{40\sqrt{3}}{2} = 20\sqrt{3}$