Given right triangle ABC, angle B=28 degrees, and side c=54.8in. Find side a.

We don't know which angle is the right angle

If it's C   we have that 

cos 28  =   a / 54.8

Multiply both sides by 54.8

54.8 cos 28  =  a ≈    48.385

If A is the right angle, we have that

cos 28  =  54.8 / a  rearrange as

a  = 54.8 / cos 28  ≈  62.06