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A 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?

A 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? Correct Answer 39

Given:

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:

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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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