Q. 164.0( 5 Votes )

# The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building.

Answer :

In the figure, let CD be the tower and AB be the building. Join the points A, D, and B, C. We get two right-angled triangles ∆ABD and ∆BCD, which are right-angled at B and D respectively. We are given that the angle of elevation of the top of the building from the foot of the tower is 30° and that of the top of the tower from the foot of the building is 60°. So, ∠CBD = 60°, ∠ADB = 30°. We are also given that the height of the tower is 60 m. Hence CD = 60 m. We need to find the height of the building, that is AB. For this, we will first find BD from ∆BDC using the trigonometric ratio tan. Using this value of BD, we will find the value of AB from ∆ABD using the trigonometric ratio tan.

In ∆BCD,

or,

So, BD = 60/√3m.

In ∆ABD,

or,

So, height of the building = AB = 20m.

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