Question

A tower and a building are on the same horizontal ground.an engineer on the top of the tower,110m high observe that the angle of elevation of the top of the building angle of depression of the foot of the building are 38°and 22° respectively

I. fine distance between the tower and the building
2.find height of the building?

Answer 1

The distance between the tower and the building is 44.44m

The height of the building is 144.72m

Explanation:

We gonna solve this problem using Pythagoras' theory and the simple use of trigonometric ratios.

1. First, we will draw 2 lines one showing a tower and the other one building, taking the smaller line as a tower and the bigger line as a building.
2. Secondly, from the tower draw 2 lines one joining the tip of the building line and the other the tip of the building line.
3. And then write the value of the angle of elevation that is 38° and the angle of depression that is 22°. (The line drawn upwards will bear the angle of elevation and the line drawn downwards will bear the angle of depression)

• Consider the lower triangle and there apply the tangent ratio that is perpendicular to the base

Let the distance between the tower and the foot of the building be x metres.

tan 22° = x/110

⇒ x = 110 x tan 22° = 110 x 0.404 = 44.44

∴ The distance between the tower and the building is 44.44 metres.

• Consider the upper triangle and there apply the tangent ratio that is perpendicular to the base.

Let the distance above the 110m in the building be y metres.

tan 38° = y/44.44

⇒ y = 44.44 x tan 38° = 44.44 x 0.7813 = 34.72m

∴ The height of the building is 110 + 34.72 = 144.72m