A bus driver driving south along a highway is 16 km from the nearest city. After traveling a distance of 32 km, the driver finds he is 19 km away from the same city. Find the bearing of the town from the second position of the motorist.

Answer 1

If we label the points order A,B,C, then we want the bearing of A from C.

Using the law of cosines, you could find the angles, and then compute the bearing.

Or, you can find that the intersection of

x^2+y^2 = 19^2
x^2 + (y+16)^2 = 32^2
is (14.1,12.7)

and now you can figure the bearing back to (0,0)