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This sounds like homework (moved to HW help) and we’re not going to do it for you.

What have you done thus far?

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Have you ever taken a trigonometry course.   If so what can you say about the angles in a right triangle with one leg twice as long as the other?  You may need a calculator with trig function and their inverse functions.

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  • 5 weeks later...

Since it has been a month, a right triangle with one leg of length 200 m and the other of length 100 m has hypotenuse of length $\sqrt{100^2+ 200^2}= \sqrt{10000+ 40000}= \sqrt{50000}$ or about 223.6 m.  That is the straight line distance from the hiker's end point back to his starting point.  the direction is $\arctan(\frac{200}{100})= \arctan(2)$ which is about 63.3 degrees east of south (so 90- 63.3= 26.7 degrees southeast).

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