Can someone help with this trig problem?
Two fire towers are 40 miles apart, tower A being due west of tower B. A fire is spotted from the towers, and the angle of elevations from A and B are 17degrees and 38degrees, respectively. Find the distance d of the fire from the line segment AB.
- ThundreLv 47 years agoFavorite Answer
Let's call the fire location F, and the closest point on AB to the fire G.
We're looking for distance d = FG. It's an altitude of triangle ABF, which means that AGF and BGF are both right angles.
Let's call the distance AG = x.
Then BG = 40-x
tan(17) = d/x
x * 0.3057 = d
tan(38) = d/(40-x)
(40-x) * 0.7813 = d
Substitute for d:
x * 0.3057 = (40-x) * 0.7813
x * 1.087 = 31.252
x = 28.75
Then put that x back into either of the original equations to get d = 8.789.