Question

Two vertical poles of heights, 20 m and 80 m stand 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

Answer 1

Correct Answer - 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`