This is a right triangle with the following dimensions:

• The adjacent side to the angle $\theta$ is $22$.
• The opposite side to the angle $\theta$ is $41.76$.
• The hypotenuse is $47.2$.

You want to find $\theta$, and we can use trigonometric functions to do so. Specifically, the tangent function relates the opposite side to the adjacent side:

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{41.76}{22}$

Now, let's compute the angle $\theta$:

$\theta = \tan^{-1}\left(\frac{41.76}{22}\right)$

I'll calculate this.The angle $\theta$ is approximately $62.22^\circ$.

Do you have any questions or need more details?

Here are 5 related questions to deepen your understanding:

1. What are the sine and cosine of the angle $\theta$?
2. How would you calculate the area of this right triangle?
3. Can you verify if the Pythagorean theorem holds for this triangle?
4. What is the length of the altitude from the right angle to the hypotenuse?
5. How would the value of $\theta$ change if the opposite side increased?

Tip: The tangent function is useful when you know the lengths of the opposite and adjacent sides in a right triangle, while sine and cosine relate the opposite/hypotenuse and adjacent/hypotenuse, respectively.