<YAC is equal to 69.5 degrees.
This is because you know the intercepted arc of <BAY is 41 degrees, making the angle 20.5 degrees (an inscribed angle is half the measure of the intercepted arc).
You also know that the radius and tangent always make a right angle (90 degrees), which mean that
<BAY + <YAC = <BAC
Or,
20.5 + x = 90
Solving for x gives you 69.5.