A man is flying in a hot air ballon in a straight line at a constant rate of 5 feet per second, while keeping it at a constant altitude. as he approaches the parking lot of a market, he notices that the angle of depression from his balloon to a friend's car in the parking lot is 35 degrees. A minute and a half later, after flying directly over this friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 36 degrees.

Sketch this problem.
It's an upside-down triangle.
Label
the
vertex
C (for car)
Label the upper left vertex B, the upper right one
A
Now, it's important to recall that in Geometry it is customary to
label the side opposite each angle with the same letter as the
angle. Do this now. You should have
Side AC = b, BC = a, and AB labeled as c
We want the length of b
We know side a is 5'/sec. X 90 sec. = 450 ft.
So, we have to use the Sine Law that uses 450 ft. and b
ft.
c / Sin C = b / Sin B
The only thing missing is angle C
Angle C = 180 - (35 + 36)
Angle C = 180 - 71
Angle C = 109 degrees

450 / Sin 109 = b / Sin 36
450 /0.8167 = b / 0.6293
Work that out to get b =346.75 ft.
346.75 ft. to the nearest whole number