A ship leaves port and sails 6 miles west. It then sails 6 miles south ;and then 6 miles west again. Approximately how many miles is the ship from port?
Created: 6 years ago |
Updated: 9 months ago
best des
Let's visualize this situation step by step:
- The ship sails 6 miles west.
- Then, it sails 6 miles south.
- Finally, it sails 6 miles west again.
Now, let's calculate the ship's distance from the starting point, which forms a right-angled triangle.
- The first 6 miles west segment and the second 6 miles west segment form the horizontal legs of the right triangle, totaling 12 miles to the west.
- The 6-mile south segment forms the vertical leg of the right triangle.
Now, we can use the Pythagorean theorem to find the length of the hypotenuse (the straight-line distance from the ship to the starting point):
c^2=a^2+b^2
Where:
- c is the length of the hypotenuse (the straight-line distance from the ship to the starting point).
- a is the horizontal leg (12 miles to the west).
- b is the vertical leg (6 miles south).
Substitute the values:
c^2=12^2+6^2
c^2=144+36
c^2=180
Now, find the square root of both sides to get c:
c=180≈13.42 miles
Rounded to the nearest whole number, the ship is approximately 13 miles from the starting point.
So, the ship is approximately 13 miles from the port. The correct answer is indeed 13, as provided in the answer choices.
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