Question

Which angle do I use to find the value for x using the tangent ratio method?

Answer 1

there's more than 1 way to skin a cat.

If you focus on the 39 deg angle, then x is "adj" to that angle and 10 is "opp."

                                 10
Then tan 39 deg = --------   Solve this for x.
                                    x                                  
                                     
                                                                                     x
If you focus on the 51 deg angle, then tan 51 deg = ------
                                                                                     10

Solve this for x.  You MUST obtain the same value for x, either way.