We will evaluate the trigonometric values for each angle:

1. $\sin 30^\circ = \frac{1}{2}$
2. $\cos 45^\circ = \frac{\sqrt{2}}{2}$

Now, add these two values:

$\sin 30^\circ + \cos 45^\circ = \frac{1}{2} + \frac{\sqrt{2}}{2}$

Since the denominators are the same, you can combine the numerators:

$= \frac{1 + \sqrt{2}}{2}$

Thus, the final answer is:

$\boxed{\frac{1 + \sqrt{2}}{2}}$

Would you like a more detailed breakdown of how I arrived at this?

Here are some related questions:

1. What is $\cos 30^\circ + \sin 45^\circ$?
2. How do you simplify $\sin 60^\circ + \cos 30^\circ$?
3. What is the exact value of $\sin 45^\circ + \cos 60^\circ$?
4. How do trigonometric values of standard angles relate to the unit circle?
5. Can you derive trigonometric values using right triangles?

Tip: Knowing standard trigonometric values (e.g., 30°, 45°, 60°) helps solve many problems quickly.