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A flag staff AB 4m high is placed on a vertical tower. The angle of elevation of foot of the flag staff  B at two points D,E on the ground level and lying on either side of foot of the tower are  α and 600 respectively with 4m and 23  m as the respective distances of these points from the foot of tower. The angle subtended by the flag staff at point D is

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a

tan−1⁡219

b

tan−1⁡29

c

tan−1⁡192

d

tan−1⁡419

answer is D.

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Detailed Solution

From ΔBCE,cot⁡60∘=23x⇒x=6 From △ACD,tan⁡(θ+α)=104=52;tan⁡α=32⇒tan⁡θ+321−tan⁡θ⋅32=52 ∵tan⁡(A+B)=tan⁡A+tan⁡B1−tan⁡Atan⁡B⇒tanθ=419⇒θ=tan−1419Therefore, the correct answer is (4).
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A flag staff AB 4m high is placed on a vertical tower. The angle of elevation of foot of the flag staff  B at two points D,E on the ground level and lying on either side of foot of the tower are  α and 600 respectively with 4m and 23  m as the respective distances of these points from the foot of tower. The angle subtended by the flag staff at point D is