Final answer:
To determine the distance north and west a fisherman is from his home port, trigonometry is used to calculate the sides of a right triangle formed by his travel path. The fisherman is approximately 10.26 miles west and 28.68 miles north from his starting point.
Step-by-step explanation:
The student has asked to determine how far north and how far west a fisherman is from his home port after traveling 30 miles in the direction N 70°W. To solve this, we can decompose the fisherman's travel into a right triangle where the fisherman's path is the hypotenuse. Using trigonometry, the fisherman's travel west (x) can be described as x = 30 × {\sin(70°)} and the travel north (y) as y = 30 × {\cos(70°)}. By calculating these, we find that:
Travel to the west (x) ≈ 10.26 milesTravel to the north (y) ≈ 28.68 miles
Hence, the fisherman is approximately 10.26 miles west and 28.68 miles north from his home port after his journey.