SAT Question bd87bc09: Right Triangles And Trigonometry answer and explanation with Desmos solution

The sine of an acute angle in a right triangle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse. In the triangle shown, $\sin (B)$ is equal to the ratio of the length of side $\overline{AC}$ to the length of side $\overline{AB}$. It's given that the length of side $\overline{AB}$ is $26$ and that $\sin (B)=\frac{5}{13}$. Therefore, $\frac{5}{13}=\frac{AC}{26}$. Multiplying both sides of this equation by $26$ yields $AC=10$. By the Pythagorean Theorem, the relationship between the lengths of the sides of triangle $ABC$ is as follows: $26^2=10^2+B{C}^2$, or $676=100+B{C}^2$. Subtracting $100$ from both sides of $676=100+B{C}^2$ yields $576=B{C}^2$. Taking the square root of both sides of $576=B{C}^2$ yields $24=BC$.