Bearing question: how far is plane when error is noticed?

[Timcago]

San Francisco International Airport (SFO) is 450 miles away from Palm Springs International Airport (PSP). The bearing from PSP to SFO is N40 degrees W. The pilot of a plane leaving PSP towards SFO mistakenly travels due north for 200 miles.

A) How far is the plane from SFO when the pilot notices the error?
B) What should his bearing be for the rest of the trip in order to arrive at SFO?
Assume a straight path.

I cannot picture this in my head. I dont understand bearings. N40 degreesW :? ?

Can anyone help me solve this?

 

[galactus]

Hey Tim:

Bearings aren't difficult once you catch on.

Here's a sketch of your problem.

Bearings are done in quadrants, as opposed to azimuths which turn a full circle clockwise.

For instance, N40W is North 40 degrees West.

If you're facing due north, turn 40 degrees toward west.

Suppose it said N40E. That's North 40 degrees East.

If you were facing due north, you would turn 40 degrees toward east.

Now, suppose it said S40E. Then, if you were facing due south, you would turn 40 degrees toward the east.

That woud be the same as if you were facing due north and turned

140 degrees clockwise.

For your problem, you can use the law of cosines to find the distance the pilot must travel in order to arrive at SFO, after his wayward flight.

\(\displaystyle \sqrt{450^{2}+200^{2}-2(450)(200)cos(40)}=323.44\)

Now, can you find the angle?.

The drawing should help.