Question

From the top of 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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Answer please.

Answer 1

Check out the attachment ☺️.

Answer 2

Answer:

7(√3+1) m

Explanation:

Let AB be the building of height 7 m and EC be the height of tower.

A is the point from where elevation of tower is 60° and the angle of depression of its foot is 45°

EC = DE + CD

also, CD = AB = 7 m

and BC = AD

In  right ΔABC,

tan 45° = AB/BC

⇒ 1= 7/BC ⇒ BC = 7 m = AD

also, In  right ΔADE,

tan 60° = DE/AD

⇒ √3 = DE/7

⇒ DE = 7√3 m

Height of the tower = EC =  DE + CD = (7√3 + 7) m = 7(√3+1) m