10. A fire is spotted from two lookout stations that are 10 miles apart. The bearing from the first lookout station to the
fire is N 52o E. The bearing from the second lookout station to the fire is N 37oW. Find the distance from each lookout
station to the fire.



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.