Question

The horizontal distance between two towers is 70m. The angle of depression of the top of the first tower when seen from the top of the second tower is 30°. If the height of the second tower is 120m, find the height of the first tower. (ans:79.58)
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Answer 1

Here is answer (78.58m).
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Answer 2

$\textbf {Theory}$ :

The figure of the given condition is attached along with the answer.

We are provided with two towers 70 m apart. The angle of depression of the top of the smaller tower from the top of the taller tower is 30°. The height of the taller tower is 120 m. We are asked to find the height of the smaller tower.

In the figure, let AB represent the shorter tower and CD represent the taller tower which is 120 m high. BD is the distance between the foot of the two towers, i.e. 70 m.

$\textbf {Solution}$ :

Lets start with solving the problem with given data now!

In Δ ACP,

tan 30° = CP / AD

1 / √3 = CP / 70

CP√3 = 70

CP = (70 / √3) m

As visible in the figure, AD || BD.

Thus, x = CD - CP

x = 120 - 70/√3

x = (120√3 - 70) / √3

$\textbf {Answer}$ :

x = 79.58 (When you take √3 = 1.73)