Question

an airplane leaves the airport and flies due west 150 miles and then 240 miles in the direction 200°40'. Assuming the earth is flat, how far is the plane from the airport at this time( to the nearest mile)?

Answer 1

I will assume that you are using the standard aircraft navigation which has 0 degrees at North and goes clockwise.
So I see a triangle with sides 150 and 240 with a contained angle of 110.666667 degrees

Using the cosine law ...

so distance^2 = 150^2 + 240^2 - 2(150)(240)cos110.66667
= 105511.0006
distance = √105511.0006
= 324.8 miles