For enrichment purposes, here's an alternate way to do the problem.  It's a
little longer, but you could do it this way if you forgot the law of sines.
Draw the altitude h from the vertex of the 114o angle. That splits the 114o angle
into the complement of 21o or 90o-21o=69o, and 114o-69o=45o. It also splits x, making

x = p+q.



Then using cosine = adjacent/hypotenuse in the rt. triangle on the left,




Then using sine = opposite/hypotenuse in the same rt. triangle,




Since the rt. triangle on the right has a 45o angle, it is 
isosceles, so q = h = 3.081964366.  Then

x = p + q = 8.028791668 + 3.081964366 = 11.11075603.

x rounds to 11.1

Edwin