Q25 of 55 Page 1

The angle of elevation of the top of a building from the foot of a 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.

Given: Height of the tower = AB = 50 m


Let height of the building = x m


In right angle triangle ABC,


tan 60° = AB/BC


∴ BC = AB/tan 60°


= (50/√3) m



Now, in right angled triangle BCD,


tan 30° = CD/BC


∴ CD = BC × tan 30°


= (50/√3) × (1/√3)


= (50/3) m


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