SAT Question 36661021: Right Triangles And Trigonometry answer and explanation with Desmos solution

Choice B is correct. By the Pythagorean theorem, if a right triangle has a hypotenuse with length $t$ and legs with lengths $r$ and $s$, then $r^2+s^2=t^2$. It's given in the right triangle shown that the legs have lengths of $9$ and $6$ and the hypotenuse has a length of $c$. Substituting $9$ for $r$, $6$ for $s$, and $c$ for $t$ in $r^2+s^2=t^2$ yields $9^2+6^2=c^2$, or $117=c^2$. Taking the square root of both sides of this equation yields $\pm \sqrt{117}=c$. Since the length of a side of a triangle must be positive, the value of $c$ is $\sqrt{117}$, which is approximately equal to $10.8167$. Of the choices, $10.8$ is the closest to the value of $c$.