solve for x. round to the nearest tenth, if necessary. answer attempt 2 out of 2 x =

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle MLK, we know the side adjacent to angle M ($ML$) and we want to find the hypotenuse ($MK = x$). We use the cosine function. $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 64^{\circ}$ and the adjacent side to $\angle M$ is $ML = 8.5$, and the hypotenuse is $x$. So, $\cos64^{\circ}=\frac{8.5}{x}$.

Step2: Solve for x

We can rewrite the equation as $x=\frac{8.5}{\cos64^{\circ}}$. Since $\cos64^{\circ}\approx0.4384$, then $x=\frac{8.5}{0.4384}\approx19.4$.

Answer:

$19.4$