Final answer:
Using the Pythagorean theorem, we computed the straight-line distance to be approximately 5.41 km after the hiker walked 4.5 km and turned 45 degrees to walk an additional 3 km. The closest answer choice provided is (C) 6.4 km.
Step-by-step explanation:
The student is asking about determining the straight-line distance from the starting point after a hiker walks a certain path. Initially, the hiker walks 4.5 km, then makes a 45-degree turn and continues for another 3 km. To find the straight-line distance, we can use the Pythagorean theorem because the path of the hiker along with the straight-line distance form a right-angled triangle.
Let's denote the straight-line distance as 'd'. The path can be broken up into two legs of a right triangle: the first leg being the 4.5 km walk and the second leg being the 3 km walk after the 45-degree turn. Using the Pythagorean theorem (a2 + b2 = c2), we calculate the straight-line distance:
- a = 4.5 km (first leg)
- b = 3 km (second leg)
- d2 = a2 + b2
- d2 = 4.52 + 32
- d2 = 20.25 + 9
- d2 = 29.25
- d = √29.25
- d ≈ 5.41 km
Therefore, the correct answer is the one closest to 5.41 km, which is option (C) 6.4 km, as it seems to be the closest provided choice.