Math problem help

Question

After a person in Kansas travels 7 miles north, then 3 miles east, and finally 3 miles south, how far is the person from the starting point?

show work to help thanks!!

Answer 1

3

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| 7 | 3

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Drawing the route, the person went 7 miles north, 3 miles east, then 3 miles south. The distance from the starting point is shown by the part of the path diagrammed in *.

Just looking at the bottom half of that figure we have a right triangle:

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And the distance from the starting point would be the hypotenuse. The upper leg would be 3 miles, the amount of miles he traveled east. The side leg would be 7 miles (amount traveled north) - 3 miles (amount traveled south) = 4 miles.

Using the Pythagorean theorem where the sum of the squares of the lengths of the legs (3**2 + 4**2) equals the square of the length of the hypotenuse, we get the square of the hypotenuse = 25, the hypotenuse equal to the square root of 25 = 5 miles, the distance from the starting point.