One day, Sofia goes hiking at a nearby nature preserve. At first, she follows the straight, clearly marked trails. From the trailhead, she travels 2.00 miles down the first trail. Then, she turns 30.0 to the left to follow a second trail for 1.00 miles. Next, she turns 160.0 to her right to follow a third trail for 2.30 miles. At this point, Sofia is getting very tired and would like to get back as quickly as possible, but all of the available trails seem to lead her deeper into the woods. She would like to take a shortcut directly through the woods (ignoring the trails).

a. What distance dSC does she have to walk to take a shortcut directly back to her starting point?

b. Through what angle θ SC should she turn to the right in order to take the shortcut directly back to her starting point?