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.

Answer 1

The height of first tower is 80m

Answer 2

Answer:

The height of the first tower is 79.58 m.

Step-by-step explanation:

Given : 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.

To find : The height of the first tower?

Solution :

We draw a rough sketch of the given situation,

Refer the attached figure below.

Let AB be the shortest tower and CD be the taller tower.

CD=120 m(given)

BD is the distance between the foot of the two towers, i.e. 70 m.

Applying trigonometric properties in triangle form,

In Δ ACP,

$\tan 30^\circ=\frac{CP}{AD}\\\\\frac{1}{\sqrt3}=\frac{CP}{70}\\\\CP=\frac{70}{\sqrt3}$

Line AD is parallel to BD, AD || BD

So, $AB=CD-CP$

$AB=120-\frac{70}{\sqrt3}$

$AB=\frac{120\sqrt3-70}{\sqrt3}$

$AB=79.58$

Therefore, The height of the first tower is 79.58 m.