SAT Question 4fb972f2: Right Triangles And Trigonometry answer and explanation with Desmos solution

It’s given that side $SQ$ is the hypotenuse of right triangle $QRS$. It’s also given that the length of side $SQ$ is $4\sqrt{82}$ and the length of side $QR$ is $4$. It follows that sides $QR$ and $RS$ are the legs of triangle $QRS$. The Pythagorean theorem states that for a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. Let $b$ represent the length of side $RS$. By the Pythagorean theorem, $4^2+b^2=(4\sqrt{82}{)}^2$, or $16+b^2=1,312$. Subtracting $16$ from both sides of this equation yields $b^2=1,296$. Taking the positive square root of both sides of this equation yields $b=36$. Therefore, the length of side $RS$ is $36$.