Question

find pq.
write your answer as an integer or as a decimal rounded to the nearest tenth.
pq =

Explanation:

Step1: Identify opposite side to $\angle Q$

The side opposite $\angle 61^\circ$ is $RP = 7$.

Step2: Use sine ratio to solve for $PQ$

$\sin(61^\circ) = \frac{RP}{PQ}$
Rearrange to solve for $PQ$: $PQ = \frac{7}{\sin(61^\circ)}$

Step3: Calculate final value

$\sin(61^\circ) \approx 0.8746$, so $PQ \approx \frac{7}{0.8746} \approx 8.0$

Answer:

$8.0$