From the top of a building 78 m high, the angles of depression of the bottom and the top of a tower are observed to be 45° and 30° respectively. Determine the approximate height of the tower so observed?

33 m

The correct answer is Option (2) → 33 m

Let the height of the tower be h m and the horizontal distance between the building and the tower be x m.

From the bottom of the tower

Angle of depression = 45°

$\tan 45^\circ = \frac{78}{x} \Rightarrow x = 78 \text{ m}$

From the top of the tower

Angle of depression = 30°

Vertical difference = 78 - h

$\tan 30^\circ = \frac{78 - h}{78}$

$\frac{1}{\sqrt{3}} = \frac{78 - h}{78}$

$78 - h = \frac{78}{\sqrt{3}} \approx 45$

$h \approx 78 - 45 = 33$