Find the bearing of a road that runs directly from A to B, with B being 3 miles north and 1.7 miles east from A?

Question

I don't understand how to find the bearing without any angles 

Answer 1

The bearing is the angle.  You have been given a right triangle.  3 miles is opposite angle A and 1.7 miles is adjacent angle A.  Graph it and you will see.

 

tan A = 3/1.7

tan A = 1.76

A = arctan 1.76

A = 60.4°

 

This angle, however, is measured from east (90°) toward north (0°).  Since a compass bearing goes clockwise from north, it must be subtracted from 90°.

 

90° - 60.4° = 29.6°

 

The bearing is 29.6°.