Answer
$$\dfrac{1}{2}$$
Work Step by Step
We apply the sum formula:
$\sin(A+B)=\sin(A)\cos(B)+\cos(A)\sin(B)$
Therefore,
$$\sin(20^\circ) \ \cos(10^\circ)+\cos(10^\circ) \ \sin(20^\circ)\\
=\sin \ (20^\circ+10^\circ)\\
=\sin \ (30^\circ)\\
=\dfrac{1}{2}$$
