If Betsy leaves Town A traveling due east for 6 miles to Town B, then turns due north and travels 9 miles to Town C, how far will her trip home be to Town A as she travels directly southwest?
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To find the distance of Betsy's trip home to Town A as she travels directly southwest, we need to use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the distance from Town A to Town C is the hypotenuse, and the distances from Town A to Town B and from Town B to Town C are the other two sides of the triangle.
We can calculate the distance from Town A to Town C using the formula:
Distance = √(AB² + BC²)
First, let's calculate AB²:
AB = 6 miles (east)
AB² = 6² = 36
Next, let's calculate BC²:
BC = 9 miles (north)
BC² = 9² = 81
Now, we can calculate the total distance from Town A to Town C:
Distance = √(36 + 81) = √117 = 10.82 miles (approximately)
Therefore, Betsy's trip home to Town A, traveling directly southwest, will be approximately 10.82 miles.