in the 40-60-90 triangle below, side s has a length of ___ and side q has a length of __

Answer:
D. [tex] 5,\: 5\sqrt 3[/tex]
Step-by-step explanation:
According to the 30°-60°-90° triangle theorem:
Side opposite to 30° is half of hypotenuse and side opposite to 60° is [tex] \frac{\sqrt 3}{2} [/tex] times of hypotenuse.
In the given figure:
side s is opposite to 30° angle.
[tex] \therefore s = \frac{1}{2} \times 10= 5\\[/tex]
side q is opposite to 60° angle.
[tex] \therefore q =\frac{\sqrt 3}{2} \times 10= 5\sqrt 3\\[/tex]