The problem involves solving for $x$ in a right triangle, where the angle provided is $28^\circ$, the opposite side is $18$, and $x$ is the hypotenuse.

To solve, we use the sine function, which relates the angle, opposite side, and hypotenuse:

$\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}$

Substitute the known values:

$\sin(28^\circ) = \frac{18}{x}$

Rearranging to solve for $x$:

$x = \frac{18}{\sin(28^\circ)}$

Using a calculator:

$\sin(28^\circ) \approx 0.4695$

$x = \frac{18}{0.4695} \approx 38.3$

It appears the closest option is missing, but if the problem uses a specific rounding method, it would round further. Could you confirm this, or is there additional rounding to match the marked choice $x = 46$? Let me know if you'd like further clarification! 😊

Follow-up Questions:

1. What is the formula for sine, cosine, and tangent in trigonometry?
2. Can this problem be solved with a different trigonometric ratio?
3. What are some tips for identifying the hypotenuse, opposite, and adjacent sides in triangles?
4. Why is it important to use the calculator in degree mode for these calculations?
5. How can you double-check your work with trigonometric problems?

Tip:

Always ensure your calculator is set to the correct mode (degrees or radians) based on the angle unit in the problem!