SAT Question 13d9a1c3: Right Triangles And Trigonometry answer and explanation with Desmos solution

Triangle $PQR$ has given angle measures of $30^{\circ }$ and $90^{\circ }$, so the third angle must be $60^{\circ }$ because the measures of the angles of a triangle sum to $180^{\circ }$. For any special right triangle with angles measuring $30^{\circ }$, $60^{\circ }$, and $90^{\circ }$, the length of the hypotenuse (the side opposite the right angle) is $2x$, where $x$ is the length of the side opposite the $30^{\circ }$ angle. Segment $\overline{PQ}$ is opposite the $30^{\circ }$ angle. Therefore, $2(PQ)=8$ and $PQ=4$.