Question

An airplane leaves and airport and flies due West 120 miles and then 150 miles in the direction south 39.17° west. How far is the plane from the airport (round to the nearest mile)

Answer 1

Okay, here we have this:

Considering the provided information we are going calculate how far is the plane from the airport, so we obtain the following using the law of cosines:

$\begin{gathered} a=\sqrt[]{120^2+150^2-2\cdot120\cdot150\cdot\cos (129.17)} \\ a\approx244\text{ miles} \end{gathered}$

Finally we obtain that the plane is approximately 244 miles far from the airport.