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# help

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Billy is hiking in Colorado. He walks eastward four miles, then turns 60 degrees northward and walks six miles and then he walks another 2 miles in the east direction. How far is he from his starting point?

pls explain

Jun 20, 2021

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A sense of direction is really important here, a graph is essential.

Basically, we find that in total, he has walked directly northward $$3\sqrt{3}$$ miles (you have to visualize/graph and 30-60-90 triangle), and directly eastward 6 miles (4+2).

Using the Pythagorean theorem, the distance from the starting point would be the hypotenuse of a right triangle with legs $$3\sqrt{3}$$ and 6, or$$\sqrt{{3\sqrt{3}}^2+6^2}$$, simplifying to $$\sqrt{27+36}$$,  $$\sqrt{63}$$,  $$3\sqrt{7}$$

In short, the answer I got was

$$3\sqrt{7}$$

Jun 20, 2021