Find the measure of the indicated angle to the nearest degree

You have a right triangle.
For the angle you are looking, 30 is the adjacent leg.
31 is the hypotenuse.
The trig ratio that relates the adjacent leg and the hypotenuse is the cosine.
Let's call the unknown angle measure x.

cos x = adj/hyp

cos x = 30/31

cos x = 0.96774

To find x, you need the inverse cosine of 0.966774.

x = 14.592

15 deg.