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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
Solution
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
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