7. In $\triangle A B C$, $A B+A C=7$, and the area of the triangle is 4, then the minimum value of $\sin \angle A$ is
Answer $\frac{32}{49}$.
Analysis From $A B + A C = 7 \Rightarrow A B \times A C \leq \frac{49}{4}$, and
$$
\frac{1}{2} A B \times A C \sin \angle A = 4 \Rightarrow \sin \angle A \geq \frac{32}{49}
$$
Equality holds when $A B = A C = \frac{7}{2}$.