solve for $x$. round to the nearest tenth, if necessary.\n\nanswer\nattempt 1 out of 2\n$x = $

Explanation:

Step1: Identify the trigonometric relationship

In the right-angled triangle $LMN$, the side $LM$ is adjacent to the angle $20^{\circ}$, and the side $LN$ (labeled $x$) is the hypotenuse.

Step2: Set up the cosine equation

The cosine of an angle is the ratio of the adjacent side to the hypotenuse. $$\cos(20^{\circ}) = \frac{52}{x}$$

Step3: Solve for $x$

Rearrange the equation to isolate $x$. $$x = \frac{52}{\cos(20^{\circ})}$$

Step4: Calculate the numerical value

Use a calculator to find the value and round to the nearest tenth. $$x \approx \frac{52}{0.93969} \approx 55.337$$

Answer:

$x = 55.3$