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Question
Two vertical poles are on either side of a road. A 30 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes angle 32°24′ with the pole and when it is turned to rest against another pole, it makes angle 32°24′ with the road. Calculate the width of the road.
Solution
Let AB the ladder and ∠ABP = 32°24 .
PQ = PB + BQ = ?
In ΔABP = sin 32°24 = `(PB)/(AB)`
PB = 30 × 0.56
PB = 16.08 m
In ΔCBQ
cos 32°24 = `(BQ)/(BC)`
BQ = 30 × 0.844
= 25.32
PQ = 16.08 + 25.32
`=>` PQ = 41.4 m
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