How do you work out bearings like how far east or north something has gone if you have the bearing it has traveled at and how far?

Answer 1

The bearing to that person or object is the heading it traveled on. Draw a right triangle by drawing an x-y coordinate plane to match East (x) and North (y) with the origin matching the point of departure. Now draw a perpendicular line from the new position to the x-axis and the hypotenuse to represent the distance traveled (r). The heading is actually the angle from north to the hypotenuse, so the angle at the origin INSIDE the triangle is its complement (angle A).

Use the sin and cos to find the x (east distance) and the y (north distance)

Sin A = y/r so, y = r (sin A) similarly x = r (cos A)