SOLUTION: An airplane traveled north for 250 mile, and west for 325 miles before reaching its destination. If it will travel straight from its starting point to its final destination, what m

Question 1108377: An airplane traveled north for 250 mile, and west for 325 miles before reaching its destination. If it will travel straight from its starting point to its final destination, what must be its bearing and how far must it travel?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

http://www.mathsteacher.com.au/year10/ch15_trigonometry/11_directions/23dir.htm

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