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JEE Advanced Mathematics question

MathematicsTrigonometric Ratio and IdentitiesJEE Advanced

A man standing between two vertical posts finds that the angle subtended at his eyes by the tops of the posts is a right angle. If the heights of the two posts are two times and four times the height of the man, and the distance between them is equal to the length of the longer post, then the ratio of the distances of the man from the shorter and the longer post is

Answer: (A),(D)

Solution

Let the man's height be ; posts are and , so their tops are and above his eye level. Let his distances from the shorter and longer posts be and ; then (distance between posts = longer post).

Let the elevation of the shorter post's top be : .

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Question ID VK-108766