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

Answer:

$6.1$

Explanation:

Step1: Identify the trig - ratio

In right - triangle $QPR$, we know the adjacent side $QP = 7$ to angle $Q = 41^{\circ}$ and we want to find the opposite side $PR$. We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. $\tan Q=\frac{PR}{QP}$

Step2: Substitute the values

We know that $Q = 41^{\circ}$ and $QP = 7$. So, $\tan41^{\circ}=\frac{PR}{7}$. Since $\tan41^{\circ}\approx0.8693$, we have $PR = 7\times\tan41^{\circ}$.

Step3: Calculate the value of $PR$

$PR=7\times0.8693 = 6.0851\approx6.1$