Hi!
We are given the information found in the picture below.
Note: The directions aren't correct, but the triangle works for this problem.
The "direct path" is the hypotenuse of this triangle.
To find this, we use the Pythagorean Theorem, where [tex]a[/tex] and [tex]b[/tex] are 2 legs of the triangle, and [tex]c[/tex] is the hypotenuse, aka the longest side of any triangle:
[tex]a^2+b^2=c^2[/tex]
We know [tex]a[/tex] and [tex]b[/tex] and want [tex]c[/tex]
[tex]4^2+5^2=c^2[/tex]
[tex]16+25=c^2[/tex]
[tex]41=c^2[/tex]
Therefore, [tex]c[/tex] is approximately [tex]6.403[/tex]
