Airport's 80482

The plane flew from airport m on a course of 132° to airport n, then from n to p on a course of 235°. The distance between the airport's mn is 380 km, np 284 km. What will be the return course to m, and what is the distance between the airport's pm?

Correct answer:

φ =  13.8016 °
n =  420.12 km

Step-by-step explanation:

φ1=132  φ2=235   p=380 km m=284 km  PNM=180(φ2φ1)=180(235132)=77   n2 = p2+m2  2 p m cos PNM  n=p2+m22 p m cosPNM=p2+m22 p m cos77° =3802+28422 380 284 cos77° =3802+28422 380 284 0.224951=420.12208 km  m2 = p2+n2  2 p n cos MPN  MPN=π180°arccos(2 p np2+n2m2)=π180°arccos(2 380 420.12213802+420.122122842)41.1984   PMN=180MPNPNM=18041.19847761.8016   φ=φ2180MPN=23518041.1984=13.8016=13°486"

Try calculation via our triangle calculator.

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators
Our percentage calculator will help you quickly calculate various typical tasks with percentages.
Do you want to convert length units?
The Pythagorean theorem is the base for the right triangle calculator.
Do you want to convert time units like minutes to seconds?
Cosine rule uses trigonometric SAS triangle calculator.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

We encourage you to watch this tutorial video on this math problem: video1   video2   video3

Related math problems and questions: