SAT Question f1251f35: Right Triangles And Trigonometry answer and explanation with Desmos solution

In triangle $XYZ$, angle $Y$ is a right angle. Therefore, triangle $XYZ$ is a right triangle. The cosine of an acute angle in a right triangle is the ratio of the length of the side adjacent to that angle to the length of the hypotenuse. In right triangle $XYZ$, side $YZ$ is the side adjacent to angle $Z$ and side $XZ$ is the hypotenuse. It’s given that the length of side $YZ$ is $560$ and the length of side $XZ$ is $565$. Therefore, $\cos Z=\frac{560}{565}$. It's also given that $\cos Z=\frac{560}{c}$. It follows that $\frac{560}{c}=\frac{560}{565}$. Therefore, $c=565$.