The value of $\theta$ is approximately $29.2^\circ$, rounded to 1 decimal place.

Would you like more details or have any other questions? Here are 5 related questions for further exploration:

1. What is the sine and cosine of $\theta$ in this triangle?
2. How can you verify this result using the Pythagorean theorem?
3. How would the value of $\theta$ change if the ratio $\frac{24}{43}$ were inverted?
4. Can you calculate the length of the hypotenuse if the opposite side is 24 units?
5. What is the angle complementary to $\theta$ in this right triangle?

Tip: The inverse trigonometric functions like $\tan^{-1}$ (arctan) help you find angles when given ratios of sides in a right triangle.