115 miles
1) Sketching this to better grasp it we have:
2) Since we could draw the route as a triangle, we can use the Law of Cosines to find out the distance between Fort Myers and Orlando:
[tex]\begin{gathered} a^2=b^2+c^2-2bc\cos (\alpha) \\ x^2=(100)^2+150^2-2(100)(150)\cos (50) \\ x^2=32500-2(100)(150)\cos (50) \\ x^2=13216.37 \\ \sqrt[]{x^2}=\sqrt[]{13216.37} \\ x\approx114.96\approx115 \end{gathered}[/tex]Note that we rounded off to the nearest tenth(114.9).
3) Hence, the answer is 115 miles
