Final answer:
The sailboat is √122 km from its starting point after traveling in a zigzag pattern first 6 km northward and then 6 km westward, followed by 5 km northward and 5 km westward.
Step-by-step explanation:
The question involves calculating the distance a sailboat is from its starting point after moving in a zigzag pattern. This involves using Pythagorean theorem to find the result, as the boat's movement creates a right-angled triangle.
First, the sailboat travels 6 km due north and then 6 km due west, making a right-angled triangle. To find the distance from the starting point at this stage, we calculate the hypotenuse (c) of the triangle with sides of 6 km each:
c = √(6^2 + 6^2) = √(36 + 36) = √72
Next, the boat travels another 5 km due north and then 5 km due west, forming another right-angled triangle. We find the hypotenuse of this second triangle in the same way:
c = √(5^2 + 5^2) = √(25 + 25) = √50
To find the total distance from the starting point, we add the two hypotenuses:
Total distance = √72 + √50 = √(72 + 50) = √122
So, the boat is √122 km from its starting point.