The horizontal distance between two poles is 15 m. The angle of depression of the top of first pole as seen from the top of the second pole is 30°. If the height of the second pole is 24 m, find the height of the first pole. [use $\sqrt{3}$ = 1.732].

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12.34 m

15.34 m

19.34 m

None of these

answer is B.

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Detailed Solution

Let AB and CD be two poles where CD = 24 m.
It is given that the angle of depression of the top of the pole AB as seen from the top of the pole CD is 30° and horizontal distance.
Question Image

between the two poles is 15 m.
∴ ∠ CAL = 30° and BD = 15 m
height of pole AB ; Let the height of pole AB be in h
AL = BD = 15 m and AB = LD = h
Therefore, CL = LD = 24 – h
Consider right Δ ACL, we have

Therefore, height of the pole AB = h = 15.34 m.

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