A pole 23 m long reaches a window which is 3√5 m above the ground on one side of street. Keeping its foot at the same point, the pole is turned to the other side of the street to reach a window 4√15 m high. What is the width (in m) of the street?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 39
The length of the pole = 23m
The first window is 3√5m above the ground and the second window is 4√15m above the ground.
In a right-angled triangle,
Base = √(Hypotenuse2 - Perpendicular2)
The width of the street = BC
In ΔABO -
BO = √(AO2 - AB2) = √[232 - (3√5)2] = √(529 - 45) = √484 = 22m
In ΔOCD -
CO = √(DO2 - DC2) = √[232 - (4√15)2] = √(529 - 240) = √289 = 17m
BC = BO + CO = 22 + 17 = 39m