A man standing on the line joining the two poles finds that the top of the poles make an angle of elevation of 60° and 45° respectively. After walking for sometime towards the other pole, the angles change to 30° and 60° respectively. The ratio of the height of the poles is:
Explanation:
Consider the image below where A and B are the initial and final position of the man. PQ and LM are the two poles of heights a and b respectively.
From ∆PQA, QA = a/Tan60 = a/√3. From ∆ALM, AM = b/Tan45 = b.
From ∆PQB, QB = a/Tan30 = a√3. From ∆BLM, BM = b/Tan60 = b/√3.
∴ [a/√3] + b = a√3 + [b/√3]
Solving we get,
a/b = [(√3) − 1]/2
Hence option (a).
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