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  • From the top of a 7 m 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.

12. From the top of a 7 m 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.

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Let the height of the cable tower be AB=h+7 m
Given,
The height of the building is 7 m and the angle of elevation of the top of the tower ∠ACE=60∘, the angle of depression of its foot ∠BCE=45∘.

According to the question,

In triangle △DBC,
tan⁡45∘=CDBD=7BD=1
BD=7 m
Since DB=CE=7 m
In triangle △ACE,
tan⁡60∘=hCE=h7=3
∴h=73 m
Thus, the total height of the tower is equal to (7+73)=7+8.732=15.7 m

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manish

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