Question

find the value of cos s rounded to the nearest hundredth, if necessary. answer attempt 1 out of 2 cos s =

Explanation:

Step1: Find the hypotenuse using Pythagorean theorem

Let the hypotenuse be $c$. In right - triangle $QRS$ with legs $a = \sqrt{7}$ and $b$, and $c = 22$. By the Pythagorean theorem $a^{2}+b^{2}=c^{2}$. We know $a=\sqrt{7}$ and $c = 22$, so $(\sqrt{7})^{2}+b^{2}=22^{2}$, $7 + b^{2}=484$, $b^{2}=484 - 7=477$, $b=\sqrt{477}$.

Step2: Use the cosine ratio

The cosine of an angle in a right - triangle is defined as $\cos S=\frac{\text{adjacent}}{\text{hypotenuse}}$. The side adjacent to angle $S$ is $\sqrt{7}$ and the hypotenuse is $22$. So $\cos S=\frac{\sqrt{7}}{22}$.

Step3: Calculate the value and round

$\sqrt{7}\approx2.646$, then $\frac{\sqrt{7}}{22}\approx\frac{2.646}{22}\approx0.12$

Answer:

$0.12$