Suppose that you see tire tracks in a dirt lot leading up to a curb. As the tire moves over the curb, it causes the tracks to end some distance, which we shall call "b", away from the curb. If the height of the curb is given as "a", find the radius of the tire in terms of a and b. To simplify the problem, we are assuming that the tire is rigid, and does not change its shape, and thus it contacts the ground and curb at exactly one point.

hints.. formula for r in terms of a and b.
use the Law of Cosines
cos (90degrees-theta)= sin (theta)
write in sin(theta) in terms of a and b.

Question

Suppose that you see tire tracks in a dirt lot leading up to a curb. As the tire moves over the curb, it causes the tracks to end some distance, which we shall call "b", away from the curb. If the height of the curb is given as "a", find the radius of the tire in terms of a and b. To simplify the problem, we are assuming that the tire is rigid, and does not change its shape, and thus it contacts the ground and curb at exactly one point.

hints.. formula for r in terms of a and b.
use the Law of Cosines  
cos (90degrees-theta)= sin (theta)
write in sin(theta) in terms of a and b.