A right triangle with a $30^\circ$ angle is a 30-60-90 triangle. Think about the fixed ratio of the three side lengths in a 30-60-90 triangle.

In the 30-60-90 ratio, the hypotenuse corresponds to the largest number. Use that to figure out how long the side opposite the $30^\circ$ angle should be when the hypotenuse is 10.

In Desmos, type 10/2 to represent half of the hypotenuse, since in a 30-60-90 triangle the hypotenuse is twice the side opposite the $30^\circ$ angle.

The numerical value that Desmos displays for 10/2 is the length of the side opposite the $30^\circ$ angle.

The triangle is right and has a $30^\circ$ acute angle, so it is a 30-60-90 triangle, a special right triangle with fixed side-length ratios.

In a 30-60-90 triangle, the sides are always in the ratio $1 : \sqrt{3} : 2$, where:

• $1$ corresponds to the side opposite the $30^\circ$ angle,
• $\sqrt{3}$ corresponds to the side opposite the $60^\circ$ angle,
• $2$ corresponds to the hypotenuse.

The hypotenuse is given as 10, and in the ratio it corresponds to $2$ units. So $2$ units in the ratio equals 10 in actual length. That means $1$ unit in the ratio (the side opposite $30^\circ$) must be $10 \div 2$.

Calculate $10 \div 2 = 5$. This is the length of the side opposite the $30^\circ$ angle, so the correct answer is 5.