If $\sin \theta=\frac{\sqrt{3}}{2}$, find the degree measure of $\theta$.

Step 1 ：The sine function gives the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. The given value, \(\frac{\sqrt{3}}{2}\), is a standard value on the unit circle, corresponding to an angle of 60 degrees or \(\frac{\pi}{3}\) radians in the first quadrant.

Step 2 ：However, the sine function is also positive in the second quadrant, so there could be another solution: 180 - 60 = 120 degrees or 180 - \(\frac{\pi}{3}\) = \(\frac{2\pi}{3}\) radians. We need to check both solutions.

Step 3 ：The calculations have returned two values for \(\theta\): approximately 60 degrees and 120 degrees. These are the two angles in the unit circle for which the sine is \(\frac{\sqrt{3}}{2}\). However, the question does not specify which quadrant the angle should be in, so both are valid solutions.

Step 4 ：Final Answer: The degree measure of \(\theta\) is either \(\boxed{60}\) degrees or \(\boxed{120}\) degrees.