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

Explanation:

Step1: Identify the trig - ratio

In right - triangle $PQ R$, we know the hypotenuse $RQ = 7$ and the angle $\angle Q=59^{\circ}$, and we want to find the adjacent side $PQ$. We use the cosine function, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. $\cos Q=\frac{PQ}{RQ}$

Step2: Substitute the values

We know that $Q = 59^{\circ}$ and $RQ = 7$. So, $\cos(59^{\circ})=\frac{PQ}{7}$. $PQ = 7\times\cos(59^{\circ})$

Step3: Calculate the value

We know that $\cos(59^{\circ})\approx0.515$. Then $PQ = 7\times0.515=3.605\approx3.6$

Answer:

$3.6$