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# In right triangle $ABC$, we have $AB = 10$, $BC = 24$, and $\angle ABC = 90^\circ$. If $M$ is on $\overline{AC}$ such that $\overline{BM}$ i

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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 $$\cos \angle ABM$$ ?

michaelcai  Nov 18, 2017
edited by Melody  Nov 19, 2017

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angle ABC is a right angle

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

Melody  Nov 19, 2017
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