A forest ranger spots a lost hiker in distress in a dense forest. The ranger is located 50 meters from a marked trail and the hiker is 80 meters into the forest and 120 meters north of the ranger's position. Determined to rescue the hiker, the ranger runs and then navigates through the dense vegetation to reach the hiker directly.
Assuming the ranger and hiker are initially at the same elevation, and the ranger's path is a straight line, how far north from their original position on the trail will the ranger enter the forest? (Hint: work out the value of y in the diagram.)