Answer: [tex]9.4\ miles[/tex]
Step-by-step explanation:
You can draw a Right triangle, as the one shown in the picture attached, where "x" is the distance between Troy and his starting point.
You need to use the Pythagorean Theorem. This is:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse, and "b" and "c" are the legs of the Right triangle.
In this case, you can identify that the legs of the Right triangle are:
[tex]a=x\\\\b=8\ mi\\\\c=5\ mi[/tex]
Therefore, you can substitute values into [tex]a^2=b^2+c^2[/tex] :
[tex]x^2=(8\ mi)^2+(5\ mi)^2[/tex]
Now you need to solve for "x" in order to find its value. This is:
[tex]x=\sqrt{(8\ mi)^2+(5\ mi)^2}\\\\x=9.43\ mi[/tex]
Finally, rounding the result to the nearest tenth of a mile, you get:
[tex]x\approx9.4\ mi[/tex]
