Question 615991
i solved this the hard way.
then i remembered the law of sines.
that made it easy (i think).
law of sines says that a/sin(A) = b/sin(B) = c/sin(C)
label the starting point of the balloon as point A.
label the ending point of the balloon as point B.
label the position of the car as point C.
the side of the triangle representing the distance the balloon travels is the side AB which we call side c because it is opposite angle C.
the side of the triangle representing the distance from where the balloon takes the 36 degree angle (point B) to the car (point C) is equal to the line segment BC which we call side a because it is opposite angle A.
we know that the side c is equal to 450 feet because the balloon travels 5 feet per second and it takes the balloon 90 seconds to go from point A to point B.
we know that angle A is equal to 35 degrees and angle B is equal to 36 degrees.
that makes angle C equal to 109 degrees because the sum of the angles of a triangle is equal to 180 degrees.
the formula we will use will be:
a / sin(A) = c / sin(C)
angle A is 35 degrees
angle C is 109 degrees
c is equal to 450 feet
a is what we want to find. 
the formula becomes:
a / sin(35) = 450 / sin(109)
multiply both sides of this equation by sin(35) to get:
a = 450 * sin(35) / sin(109)
use your calculator to solve for a to get:
a = 272.9818356
round to the nearest foot to get:
a = 273 feet
i solved it a harder way using trigonometry and got the same answer so i'm reasonably confident that it's right.
you should be able to draw yourself a diagram, but if you have problems with that, let me know and i'll send you a picture.