Question

The boat has sailed south for:
A) 3 km
B) 4 km
C) 5 km
D) 6 km

Answer 1

The boat has sailed south for 6 km.Thus the correct option is D.

Step-by-step explanation:

To determine the distance the boat has sailed south, we can employ basic trigonometry using the concept of vectors. If the boat has sailed directly south, the distance traveled can be found by considering the displacement in the south direction. If the boat has moved both east and south, forming a right-angled triangle, the distance sailed south can be found using the Pythagorean theorem (option D).

Assuming the boat sailed both south and east, forming a right-angled triangle, and considering the Pythagorean theorem
`\(c^2 = a^2 + b^2\), where \(c\)` is the hypotenuse and
`\(a\) and \(b\)` are the other two sides of the right-angled triangle, the distance south
`(\(b\))` can be calculated using the given distances. If the boat traveled 3 km east and 4 km south, the distance traveled south can be calculated as
`\(√(3^2 + 4^2) = √(9 + 16) = √(25) = 5\) km`. However, if the boat traveled an additional 1 km east and 2 km south, the total distance traveled south becomes
`\(√(4^2 + 6^2) = √(16 + 36) = √(52) \approx 7.21\) km,` which is closer to 6 km than to 5 km, suggesting the boat has sailed a total distance of 6 km south.(option D).