Final answer:
To find the southward and eastward distances the ship has traveled, we used trigonometry, specifically the sine and cosine functions, based on the bearing of S 41° E and the distance of 50 miles. The ship has traveled approximately 32.805 miles south and 37.735 miles east.
Step-by-step explanation:
To determine how many miles south and how many miles east the ship traveled, we need to break down the ship's journey into its southward and eastward components. Bearing S 41° E means the ship is traveling 41 degrees east of due south. We can use trigonometry to calculate these components using the given bearing and distance traveled.
Let's use a right triangle where the hypotenuse represents the ship's 50-mile path, the angle adjacent to the southward component is 41°, and the two legs of the triangle represent the distances south and east. Using the sine function:
- Southward distance = 50 miles × sin(41°)
= 50 miles × 0.6561
= 32.805 miles south
Using the cosine function:
- Eastward distance = 50 miles × cos(41°)
= 50 miles × 0.7547
= 37.735 miles east
Therefore, the ship has traveled approximately 32.805 miles south and 37.735 miles east.