In this problem, we are given a right triangle, and we need to find the length of side $x$ using trigonometry. Here's what we know from the triangle:

• One angle is $41^\circ$.
• The length of the opposite side (to the $41^\circ$ angle) is 9.
• The adjacent side is labeled as $x$, which we are trying to find.

Since we are dealing with a right triangle, we can use the tangent function:

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Substitute the known values into the equation:

$\tan(41^\circ) = \frac{9}{x}$

Now, solve for $x$:

$x = \frac{9}{\tan(41^\circ)}$

I'll calculate this value now.The length of side $x$ is approximately $10.35$ units when rounded to the nearest hundredth.

Would you like further details or explanations on how this was calculated?

Here are 5 related questions to explore:

1. How can you use sine or cosine to find the hypotenuse in this triangle?
2. What is the relationship between the angle and the ratio of the sides in a right triangle?
3. How would the solution change if the given angle was larger, like 60°?
4. Can you find the hypotenuse using the Pythagorean theorem with the known values?
5. How would you apply this method to solve for a missing angle?

Tip: When dealing with right triangles, always decide which trigonometric function to use (sine, cosine, or tangent) based on which sides you know and which side you're trying to find.