Answer
$DE=5$
Work Step by Step
$\triangle DEF$ is a 30-60-90 triangle. In this special triangle, the hypotenuse is twice the length of the shortest side (or the side opposite the $30^{\circ}$ angle). We are given that the hypotenuse is 10, or $FE=10$. $DE$ is the shortest side, or the side opposite the $40^{\circ}$ angle. So $DE$ is half the length of the hypotenuse, or $DE=5$.
