You are hiking on a 24-degree magnetic bearing and turn right 90 degrees to go around an obstacle. What is your new compass bearing?

When you are initially hiking on a 24-degree magnetic bearing and then turn right 90 degrees, you add 90 degrees to your current bearing. The calculation is straightforward:

Starting from 24 degrees, if you turn right and add 90 degrees, you proceed as follows:

24 degrees + 90 degrees = 114 degrees.

This result means that after making the right turn, your new compass bearing aligns at 114 degrees. Bearings are measured clockwise from north, and turning right naturally increases the numerical value of the bearing. Therefore, the new compass bearing after the right turn is indeed 114 degrees, which is accurately reflected in the correct choice.