Please help, I m having trouble understanding how to solve this. The midpoint of

I am assuming that since the triangle is named BNO, that N is the right angle.  The math works out if N is the right angle, B is the other base angle, and N is the vertex angle.  That means that "side" BO is actually the hypotenuse.  We are looking for the base length, BN.  55 degrees is the reference angle and sinde BN is adjacent to it, so along with that side and the hypotenuse, we will be using the cos ratio.  and 15000cos(55)=x. Solving for x we get x = 8603.6 or 8604 rounded.  First choice above.