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From the top of a cliff 25 m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. Find the height of the tower - Mathematics

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Sum

From the top of a cliff 25 m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. Find the height of the tower

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Solution

Let AB be the cliff and CD be the tower.

Then, AB = 25 m. From B draw BE ⊥ CD.

Let ∠EBD = ∠ACB = α.

`\text{Now, }\frac{\text{DE}}{\text{BE}}=\text{tan }\alpha \text{ and }\frac{\text{AB}}{\text{AC}}=\text{tan }\alpha \text{ } `

`\therefore \frac{DE}{BE}=\frac{AB}{AC}\text{ }So,\text{ }DE=AB [ ∵ BE = AC]`

∴ CD = CE + DE = AB + AB = 2AB = 50m

Concept: Heights and Distances
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