Question 1108377
the plane's travel forms a right triangle.


label the triangle ABC.


A is the final destination west of B.
B is the intermediate destination north of C.
C is the starting destination south of B and east of A.


this right triangle has a vertical leg from C to B which is 250 miles in length and has a horizontal leg of B to A which is 325 miles in length.


the angle formed between the direct leg from C to A and the vertical leg from C to B is the angle of interest.


this angle is equal to the arc tangent of opposite side divided by adjacent side which is AB / BC which is arc tangent of (325 / 250) which is equal to 52.43140797 degrees.


the bearing would be north 52.43140797 degrees west.


without the north west designations, the bearing would be 180 + 52... = 232.43140797 degrees.


the length of the direct route from C to A would be the square root of (250^2 + 325^2) which is equal to square root of (168125) which is equal to 410.0304867 miles.


here's a reference on bearing you might find useful.


<a href = "http://www.mathsteacher.com.au/year10/ch15_trigonometry/11_directions/23dir.htm" target = "_blank">http://www.mathsteacher.com.au/year10/ch15_trigonometry/11_directions/23dir.htm</a>