Question

Alex's house is due west of Lexington and due south of Norwood. Lexington is 6 miles from Alex's house and 8 miles from Norwood. How far is Norwood from Alex's house, measured in a straight line? If necessary, round to the nearest tenth.

Answer 1

We can use the Pythagorean theorem to solve this problem. Let's draw a diagram:

N

|\

| \

8 | \ x

| \

| \

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6 A

We know that Alex's house (A) is due west of Lexington, and due south of Norwood (N). We also know that the distance from Lexington to Alex's house is 6 miles, and the distance from Norwood to Lexington is 8 miles. We want to find the distance from Norwood to Alex's house, which we'll call x.

Using the Pythagorean theorem, we know that:

x^2 = 6^2 + 8^2

x^2 = 36 + 64

x^2 = 100

x = 10

Therefore, Norwood is 10 miles from Alex's house, measured in a straight line.