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From the top of a cliff 20 m high the angle of elevation of the top of the Tower is found to be equal to the angle of depression of the foot of the tower. What is the height of the tower?

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answer is B.

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Detailed Solution

Let the diagram of the situation be,
seo

Let the angle of elevation and angle of depression be

θ

, and the horizontal distance of the tower from the cliff be

x

. So,

∠ C A E = ∠ E A D = θ B D = A E = x

We know that the alternate interior angles are equal. So,

∠ E A D = ∠ A D B = θ

In the triangle ABD, we have

tan θ = A B D B

tan θ = 20 x

… (1)
Similarly, in the triangle AED, we have

tan θ = D E A E

tan θ = 20 A E

… (2)
Comparing the equation (1) and (2), we get

20 A E = 20 x 20 A E = 20 x A E = x

In triangle AEC, we have

tan θ = C E E A

tan θ = C E x

… (3)
Comparing the equation (1) and (3), and we have

C E x = 20 x C E = 20

Now, the length of CD is given by,

C D = C E + E D = 20 + 20 = 40

Therefore, the height of the tower is 40 m.
Hence, the correct option is 2.

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