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 45˚. Find the height of the tower. [Given √ 3 = 1.73.]

Question

Philoid · Accepted Answer

fig.21

Given –

Angle of Elevation = ∠ EAC = 60°

Angle of Depression = ∠ EAD = ∠ BDA = 45°

Height of Building = AB = ED = 7 m

In Δ ABD,

tan 45° = AB/BD

⇒ 1 = 7/BD

⇒ BD = 7 m

∴ AE = BD = 7 m [from fig.21]

And, In Δ ACE

tan ∠ CAE = CE/AE

⇒ tan 60° = CE/7

⇒ √3 = CE/7

⇒ CE = 7√3 m

Thus, Height of Tower = CE + ED = 7√3 + 7

= 7(1.73 + 1)

= 7 × 2.73

= 19.11 m