Q. 145.0( 8 Votes )
Two pillars of equal height stand on either side of a road, which is 100 m wide. The angles of elevation of the top of the pillars have measure 60 and 30 at a point on the road between the pillars. Find the position of the point from the nearest end of a pillars and the height of pillars.
Answer :
Let AB and DE be two pillars of equal height.
AB = DE
The angle of elevation of A and E from C are respectively 60⁰ and 30⁰ respectively.
∠ACB = 60⁰, ∠EDC = 30⁰ and BD = 100 m
Let BC = x
CD = BD – BC = 100 – BC = (100 – x)
In ∆ABC,
… …. (1)
In ∆EDC,
(AB = DE)
100 – x = √3AB
100√3 – AB = 3AB
4AB = 100√3
AB = 25√3
= 25 × 1.73
= 43.25 m
The height of the pillar is 43.25 m.
From equation(1),
= 25
The distance of the point from the nearest end of the pillars is 25 m and the height of each pillar is 43.25 m.
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