An elastometric bearing $($G$=130$ psi$)$ is used to support a bridge girder as shown to provide flexibility during earthquakes. The beam must not displace more than $3/8$ in when a $5$ Kip lateral load is applied as shown. Knowing that the maximum allowable shearing stress is $60$ psi, Determine

a$)$The magnitude of the angular displacement of a vertical line within the elastomer in the plane of motion of the girder is $\_\_\_\_\_$ degrees.

b$)$ The minimum required magnitude of dimension $"$a$"$ is $\_\_\_\_\_\_$ in

c$)$ The minimum allowable magnitude of dimension $"$b$"$ is $\_\_\_\_\_\_$ in $($enter answer to $6$ sig fig$)$