Question : A vertical pole and vertical tower are standing on the same level of ground. The height of the pole is 10 m. From the top of the pole, the angle of elevation of the top of the tower and the angle of depression of the foot of the tower are 60° and 30° respectively. The height of the tower is:
Option 1: 20 m
Option 2: 30 m
Option 3: 40 m
Option 4: 50 m
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Correct Answer: 40 m
Solution :
Let $AB$ be the tower and $CD$ be the pole.
$CD = BE = 10$ m
In $\triangle BCE$,
$\tan$ 30° = $\frac{10}{CE}$
⇒ $\frac{1}{\sqrt3}$ = $\frac{10}{CE}$
⇒ $CE = 10\sqrt3$
In $\triangle ACE$,
$\tan$ 60° = $\frac{h}{CE}$
⇒ $\sqrt3$ = $\frac{h}{10\sqrt3}$
⇒ $h$ = 30
So, the height of tower = 30 + 10 = 40 m
Hence, the correct answer is 40 m.
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