To solve for $x$ in the right triangle, we can use trigonometric ratios. Here’s the process:

1. Identify the known and unknown sides in relation to the given angle:

   • The given angle is $22^\circ$.
   • $x$ is the hypotenuse (the side opposite the right angle).
   • The side adjacent to the $22^\circ$ angle is $15$.

2. Choose the appropriate trigonometric function:

   • Since we know the adjacent side and want to find the hypotenuse, we use the cosine function.
   • The cosine of an angle in a right triangle is given by: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$
   • Substituting the known values: $\cos(22^\circ) = \frac{15}{x}$

3. Solve for $x$:

   • Rearrange the equation to isolate $x$: $x = \frac{15}{\cos(22^\circ)}$
   • Calculate $\cos(22^\circ)$ and solve: $x \approx \frac{15}{0.9272} \approx 16.2$

So, the value of $x$ is approximately 16.2 (rounded to the nearest tenth).

Would you like further details on this solution or have any questions?

Here are some related questions:

1. How would you find the opposite side if it were unknown?
2. What would you do if you were given the opposite side instead of the adjacent side?
3. How does the sine function differ in its application compared to cosine in right triangles?
4. Why is it important to round to the nearest tenth in some applications?
5. How can the Pythagorean theorem be used to double-check this result?

Tip: When solving for unknowns in right triangles, always label each side as opposite, adjacent, or hypotenuse based on the given angle to choose the correct trigonometric function.