Final answer:
The fire engines went to a location almost a mile away from the O'Learys' barn due to the distance, tall buildings, moonless sky, and smoky haze obstructing the direct line of sight to the flames.
Step-by-step explanation:
In the given excerpt, the fire engines went to a location almost a mile away from the O'Learys' barn because the flames were observed by the protagonist from a distance and tall buildings obstructed the direct line of sight to the fire. Additionally, the moonless sky and smoky haze made it difficult to determine the exact location of the flames. To alert the firefighters, the protagonist signaled down the speaking tube and had his assistant strike Box 342, which sent the engines to the approximate location of the fire.