Question

The angle of elevation of the top of a building from the foot of the tower is 30° and the
angle of elevation of the top of the tower from the foot of the building is 60°. If the tower
is 50 m high, find the height of the building.

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Answer 1

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Answer 2

ANSWER :–

Height of building = 50/3 m

EXPLANATION :–

GIVEN :–

• The angle of elevation of the top of a building from the foot of the tower is 30°.

• The angle of elevation of the top of the tower from the foot of the building is 60°.

• height of building is 50 m.

TO FIND :–

Height of building .

SOLUTION :–

➨ Let AB = h (height of building)

➨ In △ BCD –

=> tan(60⁰) = 50/BC

=> √3 = 50/BC

=> BC = 50/√3 m ------(1)

➨ In △ ABC –

=> tan(30⁰) = AB/BC

=> 1/√3 = h/(50/√3) ( using equation (1) )

=> h = [50/√3]× [1/√3]

=> h = (50/3) m

➨ Hence , Height of building is (50/3) m.