Since you are looking at one location (fire) from two different locations with two different bearings, you can easily draw out a triangle. Using the two angles and the 10-mile distance between the two lookout stations, we can use the sine rule to determine the distances of each station. (keep in mind that this is not a right triangle since 52° + 37° = 89°, not 90°) We solve: [sin (91°)/10] = [sin (52°)/x] --> x = 7.881 miles and for y: [sin (91°)/10] = [sin (37°)/y] --> y = 6.019 miles.
