SAT Question bbaac300: Right Triangles And Trigonometry answer and explanation with Desmos solution

Choice A is correct. The cosine of an acute angle in a right triangle is defined as the ratio of the length of the leg adjacent to that angle to the length of the hypotenuse. It's given that angle $C$ is a right angle in triangle $ABC$ and that angle F is a right angle in triangle $DEF$. Therefore, $\cos B$ is equal to the ratio of the length of side $BC$ to the length of side $AB$, and $\cos E$ is equal to the ratio of the length of side $EF$ to the length of side $DE$. It's also given that triangle $ABC$ is similar to triangle $DEF$, where angle $A$ corresponds to angle $D$. Since similar triangles have proportional side lengths, $\frac{BC}{AB}=\frac{EF}{DE}$. Therefore, the value of $\cos B$ is equal to the value of $\cos E$. Since $\cos B=\frac{1}{22}$, the value of $\cos E$ is $\frac{1}{22}$.