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Question
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?
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ANSWER : 3
Descrption
<p style="margin-left:0px;">Let's visualize this situation step by step:</p><ol><li>The ship sails 6 miles west.</li><li>Then, it sails 6 miles south.</li><li>Finally, it sails 6 miles west again.</li></ol><p style="margin-left:0px;">Now, let's calculate the ship's distance from the starting point, which forms a right-angled triangle.</p><ul><li>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.</li><li>The 6-mile south segment forms the vertical leg of the right triangle.</li></ul><p style="margin-left:0px;">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):</p><p style="margin-left:0px;"><i>c^</i>2=<i>a^</i>2+<i>b^</i>2</p><p style="margin-left:0px;">Where:</p><ul><li><i>c</i> is the length of the hypotenuse (the straight-line distance from the ship to the starting point).</li><li><i>a</i> is the horizontal leg (12 miles to the west).</li><li><i>b</i> is the vertical leg (6 miles south).</li></ul><p style="margin-left:0px;">Substitute the values:</p><p style="margin-left:0px;"><i>c^</i>2=12^2+6^2</p><p style="margin-left:0px;"><i>c^</i>2=144+36</p><p style="margin-left:0px;"><i>c^</i>2=180</p><p style="margin-left:0px;">Now, find the square root of both sides to get <i>c</i>:</p><p style="margin-left:0px;"><i>c</i>=180≈13.42 miles</p><p style="margin-left:0px;">Rounded to the nearest whole number, the ship is approximately 13 miles from the starting point.</p><p style="margin-left:0px;">So, the ship is approximately 13 miles from the port. The correct answer is indeed 13, as provided in the answer choices.</p>
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