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JEE Advanced Mathematics question

MathematicsTrigonometric Ratio and IdentitiesJEE Advanced

A flagstaff stands vertically on a pillar, the height of the flagstaff being double the height of the pillar. A man on the ground at a distance finds that both the pillar and the flagstaff subtend equal angles at his eyes. The ratio of the height of the pillar and the distance of the man from the pillar, is

Answer: (C)

Solution

Let the pillar have height , the flagstaff (top at ), and the man be at distance (eye height neglected). If each subtends , then the elevation of the pillar top is and of the flagstaff top is . Put :

θ = a, 2θ = =

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Question ID VK-108767