Final answer:
To calculate the man's distance from the starting point, we visualize his path as an 'L' shape on a plane and use the Pythagorean theorem. This results in a distance of approximately 3.61 miles, but given the options, the closest answer is 4 miles, which is option A.
Step-by-step explanation:
To find out how far the man is from the starting point after the described series of movements, we can illustrate his path as a geometrical figure on a plane. The man first travels 3 miles, then turns left and travels 6 miles, followed by another left turn and 8 miles of travel. The turns at each point make right angles, suggesting that the path looks like an 'L' shape, and therefore, we can treat this as two perpendicular vectors in a coordinate plane.
Since the final 8-mile travel is perpendicular to the original 3-mile travel, the distance from the start point is the hypotenuse of a right triangle with sides of 3 miles and (8-6) miles = 2 miles. Applying Pythagoras' theorem:
- Distance = √(3² + 2²)
- Distance = √(9 + 4)
- Distance = √13
- Distance = 3.61 miles (rounded to 2 decimal places)
However, the options provided do not contain this exact value. Upon closer inspection, we can see that a mistake may have been made either in the problem's statement or in representing the answer options. If we are strictly looking at whole numbers, the closest whole number to 3.61 is 4, suggesting option A could be the intended answer. Bearing in mind that the precision of the answer we calculated exceeds the precision of the answers offered, we must choose the closest correct option which would be option A. 4 miles.