AASL 3.3.1 Bearings | Free Mathematics Analysis and Approaches (AA) Video | RevisionDojo
Free video lessonIB · Mathematics Analysis and Approaches (AA)
AASL 3.3.1 Bearings
Learn AASL 3.3.1 Bearings in this free IB Mathematics Analysis and Approaches (AA) video lesson for SL 3.3—Angles of elevation and depression, bearings.
Learn AASL 3.3.1 Bearings in this free IB Mathematics Analysis and Approaches (AA) video lesson for SL 3.3—Angles of elevation and depression, bearings.
The video discusses bearings, a method used to determine the position of one object relative to another, particularly in navigation. Bearings are measured in degrees, starting from north and moving clockwise.
Key points include:
The bearing of B from A is found by turning from north to face B, while the bearing of A from B is the opposite direction, resulting in a difference of 180 degrees between the two.
An example is provided where the bearing of C from B is calculated as 055 degrees, and the bearing of A from C is determined to be 314 degrees through various angle relationships and calculations.
Understanding the concept of three-figure bearings is emphasized, where bearings must always be expressed in three digits to avoid confusion.
00:00Hi everybody. So in this
00:02session, we're going to look
00:03at bearings. Now bearings always
00:06cause problems for some reason.
00:09I'm going to start off
00:10the lesson by showing you
00:11
exactly what a three figure
00:13bearing is and then solving
00:17this example or going through
00:19these three questions. So firstly,
00:23what is bearing? So the
00:25common real life situation
00:28where you'll hear of bearings
00:29is in the C. So
00:32imagine you've two boats, boat
00:33A and boat B, and
00:35you want to know what
00:36position is B in relation
00:38to E, or sorry, in
00:39relation to A. Now what
00:41we use in the situation
00:43is bearings. It's one way
00:47to look at a position,
00:50and it's always the same,
00:52so that's one of the
00:53reasons why it is useful.
00:54Now what's important is
00:56we start north. So we
00:58look north. And to get,
01:03to find the bearing of
01:04B from A. Now, this
01:06is the first kind of
01:06tricky thing. B from A.
01:10If it's from A, that
01:13means we're at A and
01:15we're looking at B. So
01:16we're in boat A and
01:18we want to know what
01:19is B's position, what is
01:21the bearing of B from
01:23A?
01:24or maybe it means we're
01:25at A. Now what we
01:26do is we start here,
01:29start today, and we look
01:31north and then we always
01:33look clockwise and we turn
01:36clockwise until we get to
01:38B and there's B there.
01:41Now in a classroom what
01:42I actually do is I
01:42get students to stand up,
01:44face north and then turn
01:46clockwise to face someone else
01:47and then you find out
01:48what their bearing is. So
01:49the bearing is this angle.
01:52the angle that you turn
01:53from north to face the
01:56other person or the other
01:57boat or whatever it happens
01:58to be. Now let's say,
02:00let's just say this is
02:01120 degrees. That's 120 degrees.
02:05So the bearing of B
02:07from A is 120 degrees.
02:12Now the bearing of A
02:13from B, a little bit
02:16more tricky. What we do
02:17is again, from B,
02:20means, so let's do, we
02:22are gonna do A from
02:27B. So A from B
02:28means we are at B.
02:33So from B means we
02:34are at B. What we're
02:35gonna do is we are
02:36gonna face North. So we
02:39always start off and face
02:41North. But what we do
02:43is we're gonna turn and
02:45face and look at A
02:46and look at how many
02:48degrees
02:48need to turn. Now the
02:49common mistake is we say
02:50we're at B right, just
02:52look left and that is
02:54what 60 degrees. So the
02:55bearing is 60 degrees. Well
02:57no, because you have to
02:58turn clockwise. So we're going
03:01to face north and then
03:03we're going to do this.
03:04We're going to go all
03:05the way along here. So
03:06that's 90. That's 180 and
03:09then we go around here.
03:11And well, I don't know
03:12what that is. What we
03:13need to figure it out.
03:14Let me show you a
03:16nice trick.
03:16If I continue this line,
03:20imagine this blue line, I
03:23continue this blue line down
03:24here. What we get is
03:28this angle here is 120
03:30degrees because this is the
03:32same as this. This is
03:33a corresponding angle or an
03:35F angle which I'll explain
03:36in a second. So these
03:37angles are the exact same
03:38because these two north lines
03:41are parallel. So if this
03:43is 120,
03:44And then this angle is
03:47obviously 180 because this is
03:49straight line. The bearing of
03:51A from B is going
03:52to be 120 plus 180,
03:55which is actually 300 degrees.
03:58Now note, because of this,
04:00the bearing of A from
04:01B and the bearing of
04:02B from A are always
04:05one, there's a difference of
04:06180 degrees for this reason.
04:10Okay, so that's B from
04:11A, that's A from B.
04:12B, that's what bearings are.
04:14What I want to first
04:16just kind of explain to
04:17you is, or remind you
04:21of these angles in parallel
04:24lines. So imagine I have
04:25two parallel lines and then
04:28let's say I just draw
04:29a straight line through it.
04:31What we have here is
04:32a few rules that you
04:33may or may not be
04:34familiar with, you may have
04:35forgotten. This angle here is
04:38equal to this angle. These
04:40are called
04:40z angles and then this
04:44angle is equal to this
04:45angle because it's an opposite
04:46angle that this angle equals
04:48this angle. So all those
04:49red angles are the same
04:50and then similarly this angle
04:54here is equal to this
04:56angle here and the green
05:00angle plus the red angle
05:02has to equal 180. There
05:04was a called corresponding angles
05:05because look this plus this
05:07obviously equals 180 because
05:08It's a straight line and
05:09this is the same as
05:10this. And this is also,
05:13these are equal because these
05:15are opposite. So it's important
05:16that you know these, these
05:18rules, z angles and f
05:20angles are all turnad angles
05:22and corresponding angles are the
05:24more technical way of doing
05:26it. Okay, that's bearings. Let's
05:32look at this example. So
05:32these, these examples always cause
05:34problems. Barrings,
05:36students across the world freak
05:40out when they see it.
05:42I'm not entirely sure why.
05:44But actually, as we do
05:45this question, I'll probably find
05:47out that it's quite tricky.
05:49So find the following bearings.
05:51C from B. So here's
05:53the situation. Could, let's pretend
05:55they're both if you want.
05:57C from B, that's an
05:58easy one. If I'm at
06:02B, so it's C
06:04from B. So from B,
06:07what do I need to
06:08turn? I'm facing north. What
06:10do I need to turn
06:11to get to C? Well,
06:12it's 55 degrees. Now, I
06:16have deliberately given you this
06:18to make sure you're aware.
06:23These are often called three
06:24figure bearings. You have to
06:26put three figures. So if
06:28it's 55 degrees, you have
06:29to put 0, 5, 5
06:32degrees.
06:33Why? Just to avoid confusion.
06:38So it's always the same
06:38as always three figures. So
06:41you may or may not
06:41have seen in the movies
06:43we're at 0 .55 degrees
06:47from the other boat or
06:50whatever it happens to be.
06:52So you have to put
06:53three figures. So 0 .55
06:54degrees, fine. A from C,
06:58right? This is going to
06:58be more tricky. I might
07:00see. So from
07:01C means I'm at C.
07:03I'm going to draw a
07:04line. Now solving these problems,
07:07a bit like most trigonometry
07:09problems, if you can actually
07:11draw on the diagram and
07:13do, I advise you to,
07:14and the more kind of
07:15angles and lengths you can
07:18fill in, the easier it's
07:19going to make your life.
07:22So firstly, let's figure out
07:23what exactly we're trying to
07:24find. So we're trying to
07:25find where at C we're
07:27going to turn clockwise, all
07:29the
07:29way until we get to
07:30A. So we're trying to
07:31find that angle there, that
07:34big one. Now, this is
07:37134. If this is 134,
07:40then this one here has
07:42to be 46. This has
07:49to be 46 degrees. It's
07:5246 because this plus this
07:54has to equal 180. It's
07:56a straight line.
07:57If this is 46, this
07:59is 46. Why? Well, these
08:03are z angles, if you
08:04like, and as well, these
08:05two are corresponding, so this
08:08plus this has to equal
08:09180. Another nice little thing
08:12we can figure out is
08:13if this is 55, and
08:15this is 46, all angles
08:17in a triangle have to
08:18add up to the three
08:19angles have to add up
08:20to 180. So that is
08:2390 plus
08:2511, that is 101 plus
08:28what gives me 180, 79.
08:30So this is actually 79
08:33degrees. Now, okay, I don't
08:41actually need this 79, but
08:44I mean there was no,
08:44there was no harm me
08:45putting it in. What I
08:46want to find now is
08:48this angle here. So from
08:51here, all the way
08:53to there. So what is
08:56that? Well, it's clearly a
09:00circle minus 46. This whole
09:03thing is the full, a
09:05full turn is 360, but
09:07I want to subtract that
09:0846 because that's not part
09:09of it. So I'm going
09:10to do 360 minus 46,
09:15which gives me 314 degrees.
09:21So A from C is
09:24314 degrees. Okay, fine. I
09:31think that's the most difficult
09:32one. And yes, so now
09:34as I do these problems,
09:36I am reminded why people
09:37don't like them. They are
09:38tricky. B from C. Okay,
09:42so now I'm at C
09:43and I need to turn
09:44to B. Now remember from
09:46this one, we said there
09:49is
09:49It's always a difference of
09:51180 degrees. So imagine I
09:54drew, let's draw this line.
09:56Imagine I continued this line
09:57here. Well, this is 55,
10:01so this is 55. So
10:03it's 55 plus the 180,
10:06180 plus 55. I'll do
10:10this as part B. And
10:12then C is 180 plus
10:1655.
10:17equals 235 degrees, so this
10:23is 235 degrees. Okay, hopefully
10:27that has cleared up any
10:30issues you have with bearings.
10:32The main thing to note
10:34is you face north and
10:37you turn clockwise until you
10:40get to the place that
10:42you want to stop.
10:45you
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