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°. Determine the height of the tower.

Question

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60&deg; and the angle of depression of its foot is 45&deg;. Determine the height of the tower.

Philoid · Accepted Answer

Let us take AB = 7m,

∠ACB = 45°,

∠EAD = 60°

AB = DC and EC = ED + DC ?

In Δ ABC:

In Δ EDA,

However,

The height of tower can be calculated as:

EC = ED + DC

= 7√3 + 7

= 7(√3 +1) m