You've gone wrong at the very beginning. This is hard to explain without a diagram but I'll try. If you form a diagram where A and B are the corners of the base and that length is obviously 10. Draw a line straight up from A (know as your north line) it should be at a right angle to the base of your triangle. You've been told the fire is N25E so draw a line 25 degrees clockwise from you're north line. Call the point where the fire is F. Put in a north line from B as well. You are also told the fire is N56W of B meaning you draw a line 56 degrees anti-clockwise from B to the point F.
You have used the angles given in you formula when it should be the angles which are inside the triangle you have formed.
So the angle at A should be 90-25 = 65 and similarly with B it should be 90-56 = 34. Everything should now come out with the same answer.
Again as I said it's not easy without a diagram so ask if you didn't understand that .