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A 10 m high flagstaff stands on a tower. From a point on the level ground, the angles of elevation of the foot and top of the flagstaff are $30 ∘$ and $60 ∘$ respectively. What will be the height of the tower?

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answer is B.

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Detailed Solution

Given that, the height of the flagstaff is

10

θ = 30 °

and

α = 60 °

.
We can calculate the angle of elevation by the formula

tan θ = h e i g h t b a s e

We draw the schematic diagram,
Question Image

The distance BC form the triangle

Δ B C D

tan 30 ° = D C B C ⇒ 13 = D C B C [∵ tan 30 ° = 13] ⇒ B C = 3 D C ...... (i)

The distance DC form the triangle

Δ A B C

tan 60 ° = A D + D C B C ⇒ 3 = 10 + D C B C [∵ tan 60 ° = 3] ⇒ D C = 3 B C − 10 ...... (i i)

Substituting the value of BC from the equation (i) in equation (ii),

⇒ D C = 3 3 D C − 10 ⇒ D C 1 − 3 = − 10 ⇒ D C = 5 m

Thus, the height of the tower will be

5

m.
Therefore the correct option is 2.

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