An airplane travels due east for 1.5 hours at 400mph. Then it changes course to S 56 degrees East. Find the airplanes distnace from its point of departure and its bearing after a total fligt time of 4.5 hours.

If the plane has flown 4.5 hours, then it has traveled 1800 miles.

Draw a picture, label everything, and use the law of cosines.

Let c be the distance back to the point of departure (origin).

c=\sqrt{600^{2}+1800^{2}-2(600)(1800)cos(146)}

See why?

If the plane has flown 4.5 hours, then it has traveled 1800 miles.

Draw a picture, label everything, and use the law of cosines.

Let c be the distance back to the point of departure (origin).

c=\sqrt{600^{2}+1800^{2}-2(600)(1800)cos(146)}

See why?.


I understand that. But really when the plane was flying southeast, it only flew for 3 hours, because the question asked after a TOTAL flight time of 4.5 hours, and the plane already flew for 1.5 hours. So it flew 1200miles southeast.

But how do I find its bearing to the point of departure?

OK. Sorry about that. I misread. Just adjust the formula accordingly. Same principle.