A sailboat leaves port A and sails due east for 8 miles. It then changes course to the southeast (45-degree angle) and sails for 6 miles. Find the boat's final distance from port A.
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To find the boat's final distance from port A, we can use the Pythagorean theorem.
Let's call the point where the boat changes course point B.
After sailing due east for 8 miles, the boat is 8 miles away from port A.
If the boat sails southeast at a 45-degree angle, it forms a right triangle with sides of 6 miles and 6 miles.
Using the Pythagorean theorem, we can find the length of the hypotenuse, which represents the boat's final distance from port A.
The formula is a² + b² = c², where a and b are the lengths of the sides and c is the length of the hypotenuse.
Plugging in a = 6 miles and b = 6 miles, we get:
6² + 6² = c²
36 + 36 = c²
72 = c²
Therefore, the boat's final distance from port A is √72 miles.
Simplifying, we find that the boat's final distance from port A is approximately 8.49 miles.
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