In right triangle ABC, we have AB = 10, BC = 24, and \(\angle ABC = 90^\circ\).

If M is on \(\overline{AC}\) such that \(\overline{BM}\) is an angle bisector of \(\triangle ABC\), then what is \(\cos \angle ABM\) ?

angle ABC is a right angle

and BM bisects ABC then angle ABM is 45 degrees and cos 45 degrees = 1/sqrt2