Question

Tim sailed his boat today. He left his dock and sailed 60 kilometers south, then he turned due east and sailed another 80 kilometers. It was getting late in the day, so he turned toward the dock and sailed directly home. How far did he travel to get back to the dock? (rounded to the nearest tenth)

Options:
Option 1: 140 kilometers
Option 2: 140.6 kilometers
Option 3: 180 kilometers
Option 4: 200 kilometers

Answer 1

Using the Pythagorean theorem, the distance Tim sailed directly back to the dock can be calculated as the hypotenuse of the right triangle formed by his 60 km south and 80 km east travel, resulting in 100 km, which is not among the options provided.

Step-by-step explanation:

To figure out how far Tim sailed to get back to the dock, we can treat his journey as two perpendicular vectors - one representing the 60 kilometers south, and the other the 80 kilometers east. By using the Pythagorean theorem (a2 + b2 = c2), we can determine the distance from the dock, which is the hypotenuse of the right triangle formed by these two legs of the trip.

Here's the calculation:

• a2 = 602 km2 = 3600 km2
• b2 = 802 km2 = 6400 km2
• c2 = 3600 km2 + 6400 km2 = 10000 km2
• c = √(10000 km2) = 100 km

Therefore, the distance Tim traveled to get back to the dock is 100 kilometers, which is not listed in the given options.