Point B is 5.0 KM east of Point A. A cyclist leaves A and goes 3.0 km in a direction of 30 degrees to the north of east

Question

A. in what direction mus the rider go from this point to reach point B?

B. what distance must be covered?

please explain

Answer 1

If we let A=(0,0) then the rider ends up at C=(2.6,1.5)

Now just use the law of cosines to get the distance, and note that the angle from B to C is

tanθ = 1.5/2.6

But that is the bearing of C from B. You want the opposite direction to get from C to B.