From the top of a 7 m 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 the height of the tower.

It is given that the angle of elevation of a tower is

60 °

and angle of depression is

30 °

from the top of a 7m high building. Following figure can be constructed with the given data.

In the

Δ A O D

tan θ = P e r p e n d i c u l a r b a s e

⇒ tan 30 ° = O A A D

⇒ tan 30 ° = 7 y

(tan 30 ° = 13)

⇒ y = 713

⇒ y = 73

In the

Δ A C D

⇒ tan 60 ° = A C A D ⇒ tan 60 ° = x y

⇒ 3 = x 73

(tan 60 ° = 3)

⇒ x = 21

Now, the height of the tower,

⇒ h = 7 + x

⇒ h = 7 + 21

⇒ h = 28 m

Hence, the height of the tower is 28 m.
Therefore, the correct answer is option (2).

From the top of a $7 m$ 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 the height of the tower.