Question

From the top of a 24m high building, the angle of elevation of the top of a tower is 60 and the angle of depression of its foot is 30°. Determine the height
of the tower​

Answer 1

The height of tower is 96 m.

Step-by-step explanation:

Since we have given that

Height of building = 24 m

Angle of elevation of the top of a tower = 60°

Angle of depression of its foot = 30°

In ΔBED,

$\dfrac{24}{B}=\dfrac{1}{\sqrt{3}}=\tan 30^\circ\\\\B=24\sqrt{3}$

In ΔABC,

$\dfrac{P}{24\sqrt{3}}=\tan 60^\circ=\sqrt{3}\\P=24\sqrt{3}\times \sqrt{3}=72\ m$

So, height of the tower is given by

$24+72=96\ m$

Hence, the height of tower is 96 m.

# learn more:

From the top of 7m high building, the angle of elevation of the top of a cable tower is 60* and the angle of depression of its foot is 30* Determine height of tower

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