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?
Answer & explanation
Correct answer: option 3
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.