In an alleyway with tall buildings on both sides, a ladder of length \(3.9 \text{ m}\) leans from the foot of the west wall on the east wall, while a ladder of length \(2.5 \text{ m}\) leans the other way across the alleyway, from the foot of the east wall on to the west wall. Looking north along the alleyway, the ladders appear to cross \(1\frac{2}{7} \text{ m}\) above the roadway.

How wide is the alleyway in metres? Round your answer to 3 decimal places

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