SAT Question 16d66178: Right Triangles And Trigonometry answer and explanation with Desmos solution

Choice C is correct. The sine of an angle is equal to the cosine of its complementary angle. Since angles with measures $24^{\circ }$ and $66^{\circ }$ are complementary to each other, $\sin 24^{\circ }$ is equal to $\cos 66^{\circ }$ and $\sin 66^{\circ }$ is equal to $\cos 24^{\circ }$. Substituting $\cos 66^{\circ }$ for $\sin 24^{\circ }$ and $\cos 24^{\circ }$ for $\sin 66^{\circ }$ in the given expression yields $\left(\cos 66^{\circ }\right)\left(\cos 66^{\circ }\right)+\left(\cos 24^{\circ }\right)\left(\cos 24^{\circ }\right)$, or ${\left(\cos 66^{\circ }\right)}^2+{\left(\cos 24^{\circ }\right)}^2$.