precalc
posted by Haley on .
two observers 3 miles apart and facing each other find that the angles of the elevation of a balloon in the same vertical plane with themselves are 28degree and 31 degree respectively.find the distance from the balloon to the observer located at the 31 angle?

Label the observers A and B, with point C on the line AB, directly below the balloon, at point D.
If x is the distance CB, then since AC+CB=3,
(3x)tan28° = xtan31°
x = 1.4 miles.
Now, you want the distance DB, which is
x/DB = cos31°
DB = x/cos31° = 1.4/.857 = 1.63 miles