Question

reviewing the cosine ratio
which cosine ratios are correct for $delta pqr$? check all that apply.
$cos (p) = \frac{r}{q}$
$cos (p) = \frac{p}{q}$
$cos (q) = \frac{r}{p}$
$cos (r) = \frac{r}{p}$
$cos (r) = \frac{p}{q}$

Explanation:

Step1: Recall cosine definition

For an acute angle in a right triangle, $\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$. In $\Delta PQR$, right-angled at $Q$, hypotenuse is $q$.

Step2: Calculate $\cos(P)$

Adjacent to $\angle P$ is $r$, hypotenuse is $q$.
$\cos(P) = \frac{r}{q}$

Step3: Calculate $\cos(Q)$

$\angle Q$ is $90^\circ$, $\cos(90^\circ)=0$, so $\cos(Q)
eq \frac{r}{p}$.

Step4: Calculate $\cos(R)$

Adjacent to $\angle R$ is $p$, hypotenuse is $q$.
$\cos(R) = \frac{p}{q}$

Answer:

$\cos (P) = \frac{r}{q}$, $\cos (R) = \frac{p}{q}$