A pole 23 m long reaches a window which is $3\sqrt{5}$ 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 \sqrt{15}$ m high. What is the width (in m) of the street?

39

The width of street = BC

In triangle ABO

BO = \(\sqrt {AO×AO - AB×AB}\)

= \(\sqrt {529 - 45 }\)

= \(\sqrt {484 }\) = 22m.

In triangle OCD

CO = \(\sqrt {DO×DO - DC×DC}\)

= \(\sqrt {529 - 240 }\)

= \(\sqrt {289 }\) = 17m

Now, BC = BO + CO

⇒ 22 + 17 = 39m

Therefore, the width of the street is 39m.