find rs.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nrs =

Explanation:

Step1: Use cosine - function definition

In right - triangle $QRS$ with $\angle S = 56^{\circ}$ and hypotenuse $QS=\sqrt{65}$, and we want to find the adjacent side $RS$ to $\angle S$. We know that $\cos(S)=\frac{RS}{QS}$.

Step2: Rearrange the formula to solve for $RS$

$RS = QS\times\cos(S)$.

Step3: Substitute the given values

Since $QS = \sqrt{65}\approx 8.062$ and $\cos(56^{\circ})\approx0.559$, then $RS=\sqrt{65}\times\cos(56^{\circ})\approx8.062\times0.559\approx4.5$.

Answer:

$4.5$