Question

A road is flanked on either side by continuous rows of houses of height `4sqrt(3)` m with no space in between them. A pedestrian is standing on the median of the road facing a row house. The angle of elevation from the pedestrian to the top of the house is 30°. Find the width of the road

Answer 1

Let the midpoint of the road AB is “P” (PA = PB)

Height of the home = `4sqrt(3)` m

Let the distance between the pedestrian and the house be “x”

In the right ∆APD, tan 30° = `"AD"/"AP"`

`1/sqrt(3) = (4sqrt(3))/x`

x = `4sqrt(3) xx sqrt(3)` = 12 m

∴ Width of the road = PA + PB

= 12 + 12

= 24 m