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
+179 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
\(3\sqrt{7}\)
