To evaluate $\sin 30^\circ + \cos 45^\circ$, we can use the known values of these trigonometric functions:

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

Now, adding them together:

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

Combining the terms, we get:

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

Thus, the answer is:

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

Would you like more details, or do you have any questions?

Here are some related questions:

1. How would you compute $\sin 45^\circ + \cos 30^\circ$?
2. What is the value of $\sin 45^\circ + \cos 45^\circ$?
3. Can you find $\sin 60^\circ + \cos 30^\circ$?
4. How is the identity $\sin^2 x + \cos^2 x = 1$ useful in similar problems?
5. How would you simplify expressions like $\sin 30^\circ \cdot \cos 45^\circ$?

Tip: Memorizing common trigonometric values (like those for 30°, 45°, and 60°) can save you time in calculations.