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Question:

From the top of a 7m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

Solution:

EC=DE+CD
CD=AB=7 m
BC=AD
In △ABC, tan45°=AB/BC=CD/AD
BC=7 × 1 m=AD=7 m
AD=CD=7 m
In △ADE, tan60°=DE/AD
DE=7√3 m
Height of tower=EC=DE+CD=(7√3+7) m=7(√3+1) m