To find the value of $x$ in the given right triangle, we can use trigonometric ratios. The triangle has a right angle, a known side (13, which is adjacent to the angle), and an angle of 16 degrees. The side $x$ is the hypotenuse.

Using the cosine ratio, which relates the adjacent side and the hypotenuse in a right triangle, we have:

$\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Plugging in the known values:

$\cos(16^\circ) = \frac{13}{x}$

To find $x$, rearrange the equation:

$x = \frac{13}{\cos(16^\circ)}$

Now, calculate the value using a calculator:

1. Find $\cos(16^\circ)$.
2. Divide 13 by this cosine value.

$x = \frac{13}{\cos(16^\circ)} \approx \frac{13}{0.9613} \approx 13.5$

Thus, the value of $x$ to the nearest tenth is 13.5.

Would you like more details or have any questions?

Here are 5 related questions that build on this topic:

1. How would you find the length of the opposite side in this triangle?
2. What trigonometric ratio would you use if you were given the opposite side and the hypotenuse?
3. How can you verify that your calculated hypotenuse value is correct?
4. What is the sine of 16 degrees, and how could it be used to solve for a side in this triangle?
5. How would the calculation change if the angle were given as 74 degrees instead?

Tip: When solving right triangle problems, always identify which sides are adjacent, opposite, and the hypotenuse relative to the given angle. This will help you choose the correct trigonometric function to use.