11. Let $x, y$ be acute angles, and $x+y=60^{\circ},$ the maximum value of $\sin x+\sin y$ is
11. 1.

Since $\sin x+\sin y=2 \sin \frac{x+y}{2} \cos \frac{x-y}{2}=\cos \frac{x-y}{2}=\cos \left(x-30^{\circ}\right), x \in\left(0^{\circ}, 60^{\circ}\right)$, the maximum value of $\sin x+\sin y$ is 1.