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