Final answer:
The ship at a bearing of N 70° W has traveled approximately 9 miles north and 25 miles west after sailing for 27 miles. Trigonometric functions sine and cosine were used to find the northward and westward distances.
Step-by-step explanation:
The question involves calculating the distance traveled north and west by a ship from the port at a given bearing. The bearing of N 70° W means the ship is traveling 70° to the west of directly north. To determine the northward and westward components of the ship's journey, trigonometric functions are used, specifically the sine and cosine functions.
To calculate the northward distance (y-component), we use the cosine function since the north direction is adjacent to the angle:
Northward distance = 27 miles * cos(70°) ≈ 27 * 0.342 = 9.234 miles
Similarly, the westward distance (x-component) is calculated using the sine function:
Westward distance = 27 miles * sin(70°) ≈ 27 * 0.940 = 25.38 miles
Thus, after rounding to the nearest whole number, the ship has traveled approximately 9 miles north and 25 miles west.