Answer
a) $AC=BC=2.5ft$
b) $CM=3.54ft$
Work Step by Step
The distance from A to M is half the diameter of the circle. So, $AM=2.5ft$ and the angle $\lt AMC = 45°$ as the segment $CM$ bisects the 90° angle. The angle $\lt MAC =90°$ as well since the segment $AC$ is the tangent to the circle.
This means that we have a "special" 45°-45°-90° triangle. We know that for such a triangle, the two adjacent sides are the same and the hypotenuse equals $\sqrt{2}*side$. So, we already know all the measurements we need:
$AM=AC=BC=BM=1*2.5ft=2.5ft$
$CM=\sqrt 2 *2.5ft =3.54ft$
