SAT Question 27d075d8: Right Triangles And Trigonometry answer and explanation with Desmos solution

Choice A is correct. It’s given that for two acute angles, $\angle Q$ and $\angle R$, $\cos (Q)=\sin (R)$. For two acute angles, if the sine of one angle is equal to the cosine of the other, the angles are complementary. Therefore, the sum of the measures, in degrees, of $\angle Q$ and $\angle R$ is $90$. It’s given that the measures, in degrees, of $\angle Q$ and $\angle R$ are $x+52$ and $4x+13$, respectively. Therefore, $(x+52)+(4x+13)=90$. Combining like terms in this equation yields $5x+65=90$. Subtracting $65$ from each side of this equation results in $5x=25$. Dividing each side of this equation by $5$ yields $x=5$.