GATE EE 2024 Set 1 — Question 10
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
A surveyor has to measure the horizontal distance from her position to a distant reference point . Using her position as the center, a horizontal line segment is drawn with the two endpoints and . Points , , and are not collinear. Each of the angles and are measured as . The distance (in m) of the reference point from her position is nearest to
Correct answer
(A) 2603
Solution
Let the surveyor's position be . Since is the center of the segment , is the midpoint of , so .
In , we are given . Since the base angles are equal, is an isosceles triangle with .
In an isosceles triangle, the altitude from the vertex to the base bisects the base. Therefore, .
In the right-angled triangle :Using :The distance from her position to the reference point is approximately .
In , we are given . Since the base angles are equal, is an isosceles triangle with .
In an isosceles triangle, the altitude from the vertex to the base bisects the base. Therefore, .
In the right-angled triangle :Using :The distance from her position to the reference point is approximately .
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