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Two equal pillars on either side of a road, point between with given angles: find height or position

This type of question, asked 2 times: 3 Feb 2022 Tier II, 26 Oct 2023 Tier II. All 2 questions below, oldest first.

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  1. Question 1

    3 Feb 2022 Tier II

    92
    Two pillars A and B of the same height are on opposite sides of a road which is 40 m wide. The angles of elevation of the tops of the pillars A and B are 30∘30^\circ and 45∘45^\circ, respectively, at a point on the road between the pillars. What is the distance (in m) of the point from the foot of pillar A?

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  2. Question 2

    26 Oct 2023 Tier II

    19
    Two pillars of equal height stand on either side of a roadway which is 150 m wide. At a point in the road between pillars, the elevations of the pillars are x∘x^\circ and y∘y^\circ so that tan⁡x∘=25,tan⁡y∘=35\tan x^\circ = \frac{2}{5}, \tan y^\circ = \frac{3}{5}, then the height of each pillar is:

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