Final answer:
The total distance traveled by the hiker is calculated using the distance formula, which results in approximately 7.43 km. This value is the root of the sum of the squares of the differences in the x and y coordinates, and the closest provided answer is 7.8 km.
Step-by-step explanation:
The student has asked how to calculate the distance traveled by a hiker going from point (-3.75 km, 3.05 km) to (3.15 km, 5.80 km). To find this, we can use the distance formula which is derived from the Pythagorean theorem and applies to two-dimensional space. The distance formula calculates the distance 'D' between any two points (x1, y1) and (x2, y2) as follows:
D = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the given coordinates:
D = √[(3.15 - (-3.75))^2 + (5.80 - 3.05)^2]
D = √[(6.90)^2 + (2.75)^2]
D = √[47.61 + 7.5625]
D = √[55.1725]
D ≈ 7.43 km
Thus, the total distance traveled by the hiker is approximately 7.43 km. However, since this value is not one of the provided options, we should assess if there was any rounding during calculations or consider the closest available answer, which in this case is option a. 7.8 km.