Final answer:
To find the distance from Boat B to the boat, we can use trigonometry to calculate the distances in the east and north directions. Using the sine and cosine functions, we can find that the boat is approximately 4.97 miles from Boat B.
Step-by-step explanation:
To find the distance from Boat B to the boat, we can use the concept of trigonometry. Since the bearing of the boat from B is N64°E, we can split this into two angles: 64° to the east of north and 90° to the east of west.
We can then use the sine and cosine functions to calculate the distances in the east and north directions.
The distance in the east direction is given by 5 miles * cos(90° - 64°) = 5 miles * cos(26°).
The distance in the north direction is given by 5 miles * sin(90° - 64°) = 5 miles * sin(26°).
Using a scientific calculator, we can calculate cos(26°) ≈ 0.8988 and sin(26°) ≈ 0.4226.
Therefore, the distance from Boat B to the boat is approximately 5 miles * 0.8988 ≈ 4.494 miles in the east direction and 5 miles * 0.4226 ≈ 2.113 miles in the north direction.
Using the Pythagorean theorem, we can calculate the distance from Boat B to the boat using the formula √((4.494 miles)^2 + (2.113 miles)^2) ≈ √(20.238036 + 4.467769) ≈ √24.705805 ≈ 4.97 miles.
Therefore, the boat is approximately 4.97 miles from Boat B.