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