My kid has this problem assigned and hasn't yet learned the laws of sines and of cosines so can't be expected to use them. (The use of trig functions in a right triangle has been covered, however.)
ABC is a triangle with AB=AC. E is the midpoint of AC; D is the midpoint of BC. BE and AD meet at point N. BE=12; AD=15. Find the measure of angle BND.
I thought of using the trapezoid AEDB, the isosceles triangle AED, and/or the similar triangles CED~CAB, but don't see how any of those helps. I'm probably missing something obvious, and would appreciate your help.