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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

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