Question

Two poles standing on a horizontal ground are of heights 5 m and 10 m, respectively. The line joining their tops makes an angle of `15^(@)` with the ground. Then, the distance (in m) between the poles, is
A. `5(sqrt3+1)`
B. `(5)/(2)(2+sqrt(3))`
C. `10(sqrt(3)-1)`
D. `5(2+sqrt(3))`

Answer 1

Correct Answer - D
Given heights of two poles are 5 m and 10 m.

i.e., from figure AC = 10 m, DE = 5 m
`therefore` AB = AC - DE = 10 - 5 = 5 m
Let d be the distance between two poles.
Clearly, `DeltaABE ~ DeltaACF " [by AA- similarity criterion]"`
`therefore angleAEB = 15^(@)`
In `DeltaABE`, we have
`tan15^(@)=(AB)/(BE)implies (sqrt(3)-1)/(sqrt(3)+1)=(5)/(d)[because tan 15^(@)=(sqrt(3)-1)/(sqrt(3)+1)]`
`implies d= (5(sqrt(3)+1))/((sqrt(3)-1))`
`impliesd=5(sqrt(3)+1)/(sqrt(3)-1)xx(sqrt(3)+1)/(sqrt(3)+1)`
`=(5(3+2sqrt(3)+1))/(3-1)=(5(2sqrt(3)+4))/(2)`
`=(2xx5(sqrt(3)+2))/(2)=5(2+sqrt(3))m`