II$.$ Problems

$(27$ points$)$ Beam AB holds a UTRGV sign that weighs $375$ Ib and is supported by a steel guy wire $BC$ and a pin at $A.$ To the nearest $\frac{1}{{16}^{\text{'}\text{'}}},$ determine the diameter of the wire $BC$ if the failure normal stress is $7\mathrm{.}25$ ksi and the diameter of the double$-$shear pin A if the failure shear stress is $5\mathrm{.}82$ ksi. Assume a factor of safety of $2\mathrm{.}15.$