Find the bearing of 𝐴 from 𝐵.
We first recall that a bearing is
simply a way of measuring an angle. We remember three things. We measure from the north line, and
we always do so in a clockwise direction until we reach our line segment. In navigation, we also use three
digits. So, for example, 73 degrees as a
bearing would be 073. Now, the question here wants us to
find the bearing of 𝐴 from 𝐵. This means we’re going to be
measuring the bearing at 𝐵. So, let’s add a north line in. Now, since this diagram may not
necessarily be to scale, we’re going to use some rules for working with parallel
lines to deduce the bearing of 𝐴 from 𝐵.
Remember, we measure in a clockwise
direction from our north line round to the line segment that joins 𝐴 to 𝐵. So, that’s this angle shown. And so, to calculate this angle,
we’re going to carry the north line a little bit down from 𝐵. We know that our north lines must
be parallel and that alternate angles are equal, so we can mark this angle on our
diagram as being equal to the angle given; it’s 115 degrees. We also know that angles on a
straight line sum to 180 degrees. So, this angle that I’ve marked
along our north line is 180. It follows then that the bearing of
𝐴 from 𝐵 must be the sum of these two angles. It must be 180 plus 115. 180 plus 115 is 295. And so, we see the bearing of 𝐴
from 𝐵 is 295 degrees.