Question
Download Solution PDFA pole 23 m long reaches a window which is 3\(\sqrt5\) m above the ground on one side of a street. Keeping its foot at the same point, the pole is turned to the other side of the street to reach a window 4\(\sqrt15\) m high. What is the width (in m) of the street?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The length of the pole = 23 m
The first window is 3√5 m above the ground and the second window is 4√15 m above the ground.
Formula used:
In a right-angled triangle,
Base = √(Hypotenuse2 - Perpendicular2)
Calculation:
Here, the width of the street = BC
In ΔABO,
BO = √(AO2 - AB2)
= √(232 - 3√52)
= √(529 - 45)
= √484
= 22 m
In ΔOCD,
CO = √(DO2 - DC2)
= √(232 - 4√152)
= √(529 - 240)
= √289 = 17 m
Then, BC = BO + CO
= 22 + 17
= 39 m
∴ The width (in m) of the street is 39 m
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