posted by Allan .
Two lookout towers on Mount Abraham and Snow Mountain are 29 miles apart. A fire warden in each tower sees a forest fire. From Mount Abraham the angle formed with the line of sight to the fire and the line of sight to the other tower is 44 degrees. From Snow Mountain the fire is also observed. The angle formed from the line of sight to the fire and to the other tower is 37 degrees.
Find the distance from each tower to the fire.
Labeling the triangle vertices appropriately as A,S,F,
angle F = 180-37-44 = 99°
AF/sin37° = 29/sin99° = 29.36
SF/sin44° = 29/sin99° = 29.36
AF = 17.67
SF = 20.40