Final answer:
To find Sarah's distance and bearing from the lodge, we can use the Pythagorean theorem to calculate the total distance traveled and trigonometry to find the bearing. The distance is approximately 4.74 miles and the bearing is 61°W of north.
Step-by-step explanation:
To find the distance and bearing from the starting point to the current location of Sarah, we can break down her journey into two displacements. The first displacement is 2.1 miles at a bearing of 579°W, and the second displacement is 4.2 miles at a bearing of 518°W.
To calculate the total distance traveled, we can use the Pythagorean theorem. The total distance is the square root of the sum of the squares of the two displacements: √((2.1)^2 + (4.2)^2) ≈ 4.74 miles.
To find the bearing from the starting point to the final location, we can use trigonometry. The tangent of the angle between the total displacement and the north direction is the ratio of the east displacement to the north displacement: tan(61°) = east displacement / 4.74 miles. Solving for the east displacement gives us approximately 4.17 miles.
Therefore, the distance and bearing from the lodge to Sarah's current location is approximately 4.74 miles at a bearing of 61°W of north.