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 the foot of the tower is 30°. Find the height of the tower.
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

[FIGURE IS IN THE ATTACHMENT]

SOLUTION:
Given:
Height of the building( BD) = 7  & AE is the height of the tower.
∠ABC = 60°, ∠BED= 45°
BD = CE = 7 cm

Now from Δ BED
tan 45° = BD/DE
1 = 7/DE
DE =7
Now DE = BC = 7
In  Δ ABC
tan 60° = AC/BC
√3 = AC/7
AC = 7√3
The height of the tower(AE) = AC + CE
AE = 7√3 + 7
AE= 7(√3 + 1) m
Hence, the height of the tower is 7(√3 + 1) m

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