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From the top of a 25 m high, cliff the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. Find out the height of the tower.
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- 40 m
- 48 m
- 50 m
- 52 m
Correct Option: C
From the figure , we can see that
Let, AB be the cliff and CD be the tower. From B, draw BE ⊥ CD.
Given :- AB = 25 m
In triangle EBD and ACB , we have
| DE | = | tan α and | AB | = | tan α |
| BE | AC |
| ⇒ | DE | = | AB |
| BE | AC |
∴ DE = AB ( ∵ BE = AC)
∴ CD = CE + DE = AB + AB = 2AB = 2 x 25 = 50 m.
