Question

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

Explanation:

Step1: Recall sine ratio definition

For an acute angle in a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$

Step2: Identify sides for $\angle P$

Opposite side to $\angle P$ is $p$, hypotenuse is $q$. So $\sin(P) = \frac{p}{q}$

Step3: Identify sides for $\angle Q$

$\angle Q$ is the right angle, $\sin(90^\circ)=1$. $\frac{r}{p}
eq 1$, so this is incorrect.

Step4: Identify sides for $\angle R$

Opposite side to $\angle R$ is $r$, hypotenuse is $q$. So $\sin(R) = \frac{r}{q}$

Answer:

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