A plane flies 450 kilometers with a bearing of 316° (clockwise from north) from Naples to Elgin. The plane then flies 675 kilometers from Elgin to Canton (see figure). Canton is due west of Naples.

Question

Find the bearing of the flight from Elgin to Canton. (Round to the nearest whole number.)

_________ °

Answer 1

First, we can find the length of the North vector from Naples to Elgin with the sine law:

450/sin(90°) = x/sin(46°)

x = 450*sin(46)

Then, we can use the sine law again to find the angle between the W<->E vector and vector going from Elgin to Canton:

675/sin(90°) = 450*sin(46)/sin(θ)

θ = sin^-1(450*sin(46)/675)

The bearing angle (clockwise from north) can be calculated by subtracting the above angle from the west bearing angle of 270°:

θ' = 270 - sin^-1(450*sin(46)/675)

θ' ~ 241°