Question

An airplane pilot flies due north from Ft. Myers to Sarasota, a distance of 150 miles. She then turns N50°E and flies to Orlando, a distance of 100 miles How far is it from Ft. Myers to Orlando? Round to the nearest tenths

Answer 1

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:

`\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}`

Note that we rounded off to the nearest tenth(114.9).

3) Hence, the answer is 115 miles