Final Answer:
North: 42.40 miles, West: 37.10 miles have the boat traveled.
(option d)
Step-by-step explanation:
The boat's course is described as bearing N 37°10' W for 79.5 miles. This means the boat has traveled 79.5 miles on a course angled at 37 degrees 10 minutes west of north. To determine the distance traveled north and west, use trigonometric functions. The northward distance can be found using the sine function, as sin(37°10') = (North distance) / (Total distance).
Solving for the North distance, it equals 79.5 * sin(37°10'). Similarly, the westward distance can be found using the cosine function, as cos(37°10') = (West distance) / (Total distance). Solving for the West distance, it equals 79.5 * cos(37°10'). Thus, the northward distance is approximately 42.40 miles, and the westward distance is approximately 37.10 miles.(option d)
Trigonometry helps determine directional distances when given a bearing and total distance traveled. By utilizing trigonometric functions sine and cosine, we can calculate the components of distance in different directions (north and west in this case) based on the given bearing and total distance.
Understanding how to apply trigonometric functions in navigation, especially in determining distances and directions based on given bearings, is essential in fields like navigation, geography, and land surveying.