VII.3. Let in a triangle the equality $\frac{h_{a} \cdot h_{b}}{h_{c}}=c$ holds, where $h_{a}, h_{b}$, and $h_{c}$ are the altitudes, and $c$ is a side of the triangle. Determine the measure of one of the interior angles of the triangle.
Solution: It is known that $a \cdot h_{a}=b \cdot h_{b}=c \cdot h_{c}=2 P$, i.e., $h_{a}=\frac{2 P}{}$; $h_{b}=\frac{2 P}{b}$; $h_{c}=\frac{2 P}{c}$. If we substitute in the given equation, we have: $\frac{2 P \cdot c}{a \cdot b}=c$; $P=\frac{a \cdot b}{2}$, i.e., the triangle is a right triangle. One angle is $90^{\circ}$.