Final answer:
Without specific distances for the leg of the journey from point B to point C and back to A, the total distance cannot be numerically calculated, but involves adding each leg's distance.
Step-by-step explanation:
The correct answer is option "total distance covered by the boat" is calculated by adding the distance of each leg of the journey. Initially, the boat travels 8 miles north from point A to point B. The subsequent directions are vector movements and will require the use of trigonometry or graphical methods to solve.
However, the question does not provide the distances for the other legs of the journey, so a numeric total distance cannot be given without additional information.
If the directions after point B form a straight line back to point A, the boat would have covered the same distance southwards as northwards which is 8 miles, and then a diagonal leg which requires more information to calculate.
To calculate the total distance covered by the boat, we need to find the distance between point A and point C.
Using the concepts of vectors and trigonometry, we can break down the boat's motion into horizontal and vertical components.
The horizontal component is given by the distance traveled south, which is 8 miles.
The vertical component is given by the distance traveled west, which can be calculated using trigonometry.
The magnitude of this component is 8 miles * sin(40 degrees) = 5.15 miles.
The total distance covered is the hypotenuse of a right triangle formed by the horizontal and vertical components.
Using the Pythagorean theorem, the total distance is sqrt((8 miles)^2 + (5.15 miles)^2) = 9.8 miles (rounded to one decimal place).