While following directions on a treasure map, a person walks 45.0 m south, then turns and walks 7.50 m east. which single straight-line displacement could the person have walked to reach the same spot? a. 45.6 m at 80.5° south of east b. 52.5 m at 9.5° south of east c. 45.6 m at 9.5° south of east d. 52.5 m at 80.5° south of east

The correct answer is C. The person could have walked in a straight 45.6 m line 9.5° south of east to get to the same spot.

You can imagine the person's south and east walking distances as being two sides of a right triangle. The other side of the triangle, the hypotenuse, is the shortest distance between the two starting and end points in the person's travel.

Because two sides of this right triangle are known, you can plug these values into the Pythagorean theorem (below) to solve for the missing side , which will be the answer to the question.



The question also asks you to find the degrees south of east the person walked, θ, (see the attached diagram). You can find this angle by doing the following operations:

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