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Two vertical poles of heights, 20 m and ...

Two vertical poles of heights, 20 m and 80 m stand 50m apart on a horizontal plane. The height (in m) of the point of intersection of the lines joining the top of each pole to the foot of the other, from this horizontal plane is

A

15

B

16

C

12

D

18

Text Solution

Verified by Experts

The correct Answer is:
B
Let a first pole AB having height 20 m and second pole PQ having height 80 m
and `anglePBQ = alpha, angleAQB = beta`

and MN = hm is the height of intersection point from the horizontal plane
`because tan alpha=(h)/(x)=(80)/(x+y)["in "DeltaMNB and DeltaPQB]...(i)`
and `tanbeta=(h)/(y)=(20)/(x+y)" "["in" DeltaMNQ and DeltaABQ]" ...(ii)"`
From Eqs. (i) and (ii), we get
`(y)/(x) = 4 implies y = 4x " ...(iii)"`
From Eqs. (i) and (ii), we get
`(h)/(x)=(80)/(x+4x)implies h = (80)/(5) = 16m`
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