To solve for the angle $\theta$ in the given right triangle, we can use the tangent function. The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. Here, the opposite side to angle $\theta$ is 14 cm, and the adjacent side is 9 cm.

The formula for tangent is: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Substitute the given values: $\tan(\theta) = \frac{14}{9}$

Now, to find $\theta$, we take the arctangent (inverse tangent) of $\frac{14}{9}$: $\theta = \tan^{-1}\left(\frac{14}{9}\right)$

Using a calculator to find the arctangent: $\theta \approx \tan^{-1}(1.5556)$ $\theta \approx 57.99^\circ$

Rounding to the nearest integer: $\theta \approx 58^\circ$

So, the size of angle $\theta$ is approximately $58^\circ$.

Would you like any additional details or have any questions?

Here are some related questions:

1. How do you use the sine function to find the hypotenuse in a right triangle?
2. What is the relationship between the angles in a right triangle?
3. How can the Pythagorean theorem be used to find the length of the hypotenuse?
4. What are the definitions of the sine and cosine functions in a right triangle?
5. How can you convert degrees to radians?

Tip: Always ensure your calculator is set to the correct mode (degrees or radians) depending on the unit you need for your angle measurements.