# Problem of the Week Problem C Altitude Change

In acute $$\triangle ABC$$, two altitudes have been drawn in. Point $$M$$ lies on $$AB$$ so that $$CM$$ is an altitude of $$\triangle ABC$$, and point $$N$$ lies on $$AC$$ so that $$BN$$ is an altitude of $$\triangle ABC$$.

Suppose $$CM=32$$ cm, $$AB=36$$ cm, and $$AC= 40$$ cm. Determine the length of altitude $$BN$$.

Note: An altitude of a triangle is the line segment drawn from a vertex of the triangle perpendicular to the opposite side.

Theme(s): Geometry, Number Sense