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Q.5 in this month's dive magazine...
How many degrees would you turn to navigate an equilateral triangle?
120???
Steve Walker
18-03-2003, 17:32
Q.5 in this month's dive magazine...
How many degrees would you turn to navigate an equilateral triangle?
120???
Haven't seen it yet, but they taught us at school that the internal angles of a triangle add up to 180 degrees, of course that was a very, very long time ago and things may have changed since then... ;)
They may have meant how many degrees in total to get back to your starting point? in which case 2 x 60 = 120 in total.
Do kids still do multiplication at school?
Cheers
Nick McV
18-03-2003, 17:37
How many degrees would you turn to navigate an equilateral triangle? 120???
This one caught me out way back in basic training...
All the angles in a triangle add up to 180 (a straight line).
As you turn round the 60 deg angle of the equilateral triangle, you have in fact turned yourself from your straight heading through everything BUT the 60 deg (180-60=120).
Therefore if you navigate all the way round the equilateral triangle, you will have turned through 3*120 =360 - a full circle.
It helps to draw it and extend the lines so you can write in all the angles. Hope this helps....
Q.5 in this month's dive magazine...
How many degrees would you turn to navigate an equilateral triangle?
120???
It depends what question you're asking here and indeed, what question Dive are asking. (I can't remember the exact wording offhand).
If the question is:
How many degrees would you turn after each triangle side in order to navigate an equilateral triangle?
then this is the answer:
120 deg. Draw out the triangle you would dive along. Each time you come to an apex, extend the line slightly. You'll see that the angle this extended line makes with the next directional line in 120 deg.
Another way of looking at it - for an equilateral triangle you need to get back to the same point by travelling 3 equivalent distances, and turning 3 equivalent angles. There are 360 deg in a full rotation ( which, effectively you are making), so 360/3 = 120.
If however the question is as you have written it, i.e.
How many degrees would you turn to navigate an equilateral triangle?
then the answer could arguably be 360. (120+120+120)
I don't know how far you've got in your BSAC career, but you'll (unfortunately) probably learn that BSAC questions are riddled with ambiguities, tricks and stumbling blocks. I thought some of this month's DIVE questions were written in fantastically typical BSAC style - poorly worded and some (arguably) multiple-possible answers. (As well as having two wreck descriptions with no actual photographs of the wreck - seemed like a bout of armchair journalism?)
It was only a little moan.....
T
I believe its common knowledge that BSAC have little or no input to the mag, else why publish 'dont give oxygen' then retract it!
Matt
Philip Smith
18-03-2003, 19:35
Another way of looking at it - for an equilateral triangle you need to get back to the same point by travelling 3 equivalent distances, and turning 3 equivalent angles.
Well no, you only need to turn through 120 degrees twice to complete the triangle. At the moment of completion, you are not facing in the same direction as when you started.
How many degrees would you turn to navigate an equilateral triangle?
then the answer could arguably be 360. (120+120+120)
The answer in that case would be 240 degrees!
PS
:=How many degrees would you turn to navigate an equilateral triangle? 120???
This one caught me out way back in basic training...
All the angles in a triangle add up to 180 (a straight line).
As you turn round the 60 deg angle of the equilateral triangle, you have in fact turned yourself from your straight heading through everything BUT the 60 deg (180-60=120).
Therefore if you navigate all the way round the equilateral triangle, you will have turned through 3*120 =360 - a full circle.
It helps to draw it and extend the lines so you can write in all the angles. Hope this helps....
This can be extended for any regular polygon
It can be proven that the sum of the exterior angles of a polygon is 360 degrees, therefore the number of degrees turned for any regular polygon will be 360 / n , where n is the number of sides of the polygon
Therefore for a triangle, as you say, the angles turned will be 360/3 = 120
For a square course, 360 / 4 = 90
for a octogon course, 360 / 8 = 45
for a dodecagon, 360/12 = 30
To work out the total degrees turned returning to a start point will be 360 - ( 360 / n ) ( since you do not have to turn when arriving back at the start point.
etc.
:=Another way of looking at it - for an equilateral triangle you need to get back to the same point by travelling 3 equivalent distances, and turning 3 equivalent angles.
Well no, you only need to turn through 120 degrees twice to complete the triangle. At the moment of completion, you are not facing in the same direction as when you started.
Ahhh...details details - If you want to get back to the same place AND face the same direction ;)
T
Andy Wade
19-03-2003, 09:09
:=:=Another way of looking at it - for an equilateral triangle you need to get back to the same point by travelling 3 equivalent distances, and turning 3 equivalent angles.
:=
:=Well no, you only need to turn through 120 degrees twice to complete the triangle. At the moment of completion, you are not facing in the same direction as when you started.
:=
Ahhh...details details - If you want to get back to the same place AND face the same direction ;)
Oh dear,
Am I alone in thinking that this thread just illustrates how hard it can be to ask what would appear to be a very simple question?
And also that the most important thing from an examinees point of view is to read the question carefully and answer exactly what it is asking.
Assuming you can actually understand it of course.....
Just a point about the question, I'd have thought that from a practical and divers point of view, they would only turn twice in an equilateral triangle before heading back to the start point on the final bearing. I've never asked anyone to turn again to face in the direction of the original heading.
Two times 60 degrees or (120 degrees if you want to be pedantic)
It should be 120 degrees total.
What was the question again?
Just a point about the question, I'd have thought that from a practical and divers point of view, they would only turn twice in an equilateral triangle before heading back to the start point on the final bearing. I've never asked anyone to turn again to face in the direction of the original heading.
Depends on the trainees, some of them seem to end up facing that direction anyway ;)
Two times 60 degrees or (120 degrees if you want to be pedantic)
It should be 120 degrees total.
Two times 60 deg? Do you not mean two times 120 deg? The internal angle is 60, but a person rotating will turn through the external angle (180-60) i.e. 120 deg. Do it twice to get back to the same point....
Are we answering different questions?
T
Andy Wade
19-03-2003, 10:24
:=Just a point about the question, I'd have thought that from a practical and divers point of view, they would only turn twice in an equilateral triangle before heading back to the start point on the final bearing. I've never asked anyone to turn again to face in the direction of the original heading.
Depends on the trainees, some of them seem to end up facing that direction anyway ;)
:=Two times 60 degrees or (120 degrees if you want to be pedantic)
:=It should be 120 degrees total.
Two times 60 deg? Do you not mean two times 120 deg? The internal angle is 60, but a person rotating will turn through the external angle (180-60) i.e. 120 deg. Do it twice to get back to the same point....
Are we answering different questions?
Probably.
OK let me ask you this question.....
When navigating a square would you turn through 270 degrees on each corner or 90 degrees on each corner?
Depends on how you teach the exercise or ask the question, doesn't it?
I teach people to turn 90 degrees three times to navigate a square.
Doing it the other way makes it harder for the trainee to visualise it.
IMHO of course.
Are you navigating around the inside or the outside of the triangle?
Now I'm confused.
;-)
.
john kendall
19-03-2003, 10:27
:=
:=:=Just a point about the question, I'd have thought that from a practical and divers point of view, they would only turn twice in an equilateral triangle before heading back to the start point on the final bearing. I've never asked anyone to turn again to face in the direction of the original heading.
:=
:=Depends on the trainees, some of them seem to end up facing that direction anyway ;)
:=
:=:=Two times 60 degrees or (120 degrees if you want to be pedantic)
:=:=It should be 120 degrees total.
:=
:=Two times 60 deg? Do you not mean two times 120 deg? The internal angle is 60, but a person rotating will turn through the external angle (180-60) i.e. 120 deg. Do it twice to get back to the same point....
:=
:=Are we answering different questions?
:=
Probably.
OK let me ask you this question.....
When navigating a square would you turn through 270 degrees on each corner or 90 degrees on each corner?
Depends on how you teach the exercise or ask the question, doesn't it?
I teach people to turn 90 degrees three times to navigate a square.
Doing it the other way makes it harder for the trainee to visualise it.
IMHO of course.
Um, No, You turn 90 deg for a square, however if you turned 60 deg each corner, you would end up doing a hexagon. For a triangle you need to turn 120deg.
Draw it out, it's the easiest way to see it.
John
Iain Crampton
19-03-2003, 10:31
:=
:=:=Just a point about the question, I'd have thought that from a practical and divers point of view, they would only turn twice in an equilateral triangle before heading back to the start point on the final bearing. I've never asked anyone to turn again to face in the direction of the original heading.
:=
:=Depends on the trainees, some of them seem to end up facing that direction anyway ;)
:=
:=:=Two times 60 degrees or (120 degrees if you want to be pedantic)
:=:=It should be 120 degrees total.
:=
:=Two times 60 deg? Do you not mean two times 120 deg? The internal angle is 60, but a person rotating will turn through the external angle (180-60) i.e. 120 deg. Do it twice to get back to the same point....
:=
:=Are we answering different questions?
:=
Probably.
OK let me ask you this question.....
When navigating a square would you turn through 270 degrees on each corner or 90 degrees on each corner?
Um.. 90 degrees *is* the external angle on a square (180-90=90), the angle is the one between the direction you are facing at the start of the turn and at the end of the turn, i.e. the angle you actually turn through, which is the the easiest (IMHO) way to think about it, thus for a square at each corner it is 90 degrees, for an equilateral triangle it is a bit further as youstart to come back on yourself - 120 degrees.
Iain C.
OK let me ask you this question.....
When navigating a square would you turn through 270 degrees on each corner or 90 degrees on each corner?
90, of course, but 270 in the opposite direction will still get you there ...
Depends on how you teach the exercise or ask the question, doesn't it?
Well ... erm ... sort of. The square is awkward, because it just so happens that the external angle = internal angle. (180 - 90 = 90) It needs to be made clear to the trainee that it's the external angle that you're turning through, so they can extrapolate to other shapes.
I teach people to turn 90 degrees three times to navigate a square.
Doing it the other way makes it harder for the trainee to visualise it.
Of course - everyone does. That's because the external angle is 90 deg.
Are you navigating around the inside or the outside of the triangle?
Either - the angles are the same! I think a more important question is how often do divers regularly dive polygons?
T
Steve Walker
19-03-2003, 11:50
But we all know that the answer to everything is 42 ;)
Cheers
Steve
Philip Smith
19-03-2003, 14:25
:=Ahhh...details details - If you want to get back to the same place AND face the same direction ;)
Oh dear,
Am I alone in thinking that this thread just illustrates how hard it can be to ask what would appear to be a very simple question?
It's not necessarily hard, it just needs some care to avoid ambiguity, which our magazine appears to be failing to apply on a regular basis.
PS
John Williams
19-03-2003, 15:42
Andy,
With the triangle it does not matter whether you navigate the inside or the outside - you must still turn through 120*
From 000* onto 120* (or 240*) and then onto 240* or (120*)
If you turn through 60* then you'd need to navigate your "triangle" twice to get back to the same point ...after travelling round a hexagon!
It's the angle you turn through that counts - not the schoolboy maths that says the internal angles add to 180*.
HTH
John
It's not necessarily hard, it just needs some care to avoid ambiguity, which our magazine appears to be failing to apply on a regular basis.
Which (probably proved by all the threads) was the point I was making - just asked my question in a way so as to see if it wasn't just me finding fault with the question...
It's not necessarily hard, it just needs some care to avoid ambiguity, which our magazine appears to be failing to apply on a regular basis.
Which (probably proved by all the threads) was the point I was making - just asked my question in a way so as to see if it wasn't just me finding fault with the question...
The question as posed is perfectly correct and unambiguous. If you answer the question asked then you will get the answer given
"How many degrees would you turn to navigate an equilateral triangle?"
To navigate an equilateral triangle....
An equilateral triangle is a regular 3 sided polygon.
The external angles for a polygon add up to 360 degrees
Given 3 sides, then the angle turned will be 360/3 = 120 degrees.
Unlike many BSAC questions, this is a perfectly well written question.
Dave
Philip Smith
19-03-2003, 19:20
The question as posed is perfectly correct and unambiguous. If you answer the question asked then you will get the answer given
"How many degrees would you turn to navigate an equilateral triangle?"
No, the question is ambiguous because it is not clear whether it means the number of degrees turned at each corner or the degrees turned in navigating the whole triangle (which could involve two or three corners depending on your defintion of completion). The answer given indicates they meant the turn at each corner, but to me, "navigate an equilateral triangle" reads more like the complete exercise.
PS
Mike Halligan
19-03-2003, 19:41
The question as posed is perfectly correct and unambiguous. If you answer the question asked then you will get the answer given
:=
:="How many degrees would you turn to navigate an equilateral triangle?"
Strikes me that both Maths and English are suspect, but in the reader rather than in the question as posed. It is, as I think Dave said, totally unambiguous and has but two correct answers, which any BSAC Instructor is well capable of interpreting.
To navigate a polygon completely (to go around and end up facing just as you were before starting) you must turn 360 deg.
To navigate a triangle of equal sides and therefore equal angles can require a turn of only 240 degrees. This brings you back to your starting point, albeit facing at 120 degrees to your original orientation.
God help us when we move onto real navigation! Is it April 1st yet?
Mike
David J Smith
19-03-2003, 23:37
Q.5 in this month's dive magazine...
How many degrees would you turn to navigate an equilateral triangle?
120???
I may be wrong but isn't the real fact that dive magazine is just that, a magazine. So precise, as opposed to correct wording probably isn't that important, especially when the answers are at the bottom of the page. Who knows, if all those trainees out there are that confused, they may ask your advice and then all you instructors are presented with an ideal teaching opportunity! Otherwise it has completed a different job of promoting discussion amongst some well trained mathmaticians and English scholars.
Philip Smith
20-03-2003, 00:32
It is, as I think Dave said, totally unambiguous and has but two correct answers, which any BSAC Instructor is well capable of interpreting.
Mike, I hope this is in jest. If there are "but two correct answers", the question is ambiguous!
To navigate a polygon completely (to go around and end up facing just as you were before starting) you must turn 360 deg.
To navigate a triangle of equal sides and therefore equal angles can require a turn of only 240 degrees.
You make my point. Both of these answers have been identified as potentially correct earlier in this thread, but neither of them was offered in Dive's multi-choice!
cheers,
Phil.
Andy Wade
20-03-2003, 08:38
:=Q.5 in this month's dive magazine...
:=
:=How many degrees would you turn to navigate an equilateral triangle?
:=
:=120???
I may be wrong but isn't the real fact that dive magazine is just that, a magazine. So precise, as opposed to correct wording probably isn't that important, especially when the answers are at the bottom of the page. Who knows, if all those trainees out there are that confused, they may ask your advice and then all you instructors are presented with an ideal teaching opportunity! Otherwise it has completed a different job of promoting discussion amongst some well trained mathmaticians and English scholars.
Not to mention the odd thicky instructor who ought to know better....
I'm getting my coat and I may be gone for some time. Well, at least until tomorrow anyway.
Oh, the shame of it!
_(8)o
.
Strikes me that both Maths and English are suspect, but in the reader rather than in the question as posed. It is, as I think Dave said, totally unambiguous and has but two correct answers, which any BSAC Instructor is well capable of interpreting.
"Totally unambiguous and has but two correct answers" - that's a classic, Mike! However, this wouldn't be a problem, if instead of multi-guess questions, they were short answer questions. Regardless of the students take on the question, the instructor can read the thought process and mark accordingly.
But we don't have this. We have multiguess. Therefore the questions MUST be written in such a manner as to be have one correct answer. Why do we have multiguess?
- Easy to mark, so saves time.
- Easier to do - the answers are all on the paper.
- Less paperwork - one question sheet each (reusable) and one answer sheet each.
The downside of multiguess is the because of the nature of the exam, the questions have to totally unambiguous and written in such a way as it is difficult to misinterpret the question. The student doesn't get a chance to explain his/her thinking behind an answer. Therefore BSAC owe it to the trainees to write questions that can only have one possible right answer.
I'd like to waffle on more, but it's coffee time!
T
Steve Walker
20-03-2003, 12:29
I may be wrong but isn't the real fact that dive magazine is just that, a magazine. So precise, as opposed to correct wording probably isn't that important...
A fair point about promoting discussion, but without getting into the anti-Dive type of thread we had recently, I think the magazine occupies a reasonably important role for BSAC, just look at how much discussion it provokes on these forums.
Firstly it says clearly it is BSACs "Official Journal" (though on closer inspection the actual definition of that may not always mean what some may think it means) and its stated aims are to "entertain AND inform" (quote from Council), so in terms of "informing" on theory I think we are correct to be as analytical as above.
As I recently communicated to Dive's editor, I've always thought that testing your own theory levels should be given a little more importance in the mag. Rather than being a relatively obscure bit at the back which probably gets overlooked by many, it should, like diving theory itself, be more central to our thinking. Why not give it more gravitas so that its contents could be an adjuct for instructors?
It would be useful to direct trainees to the quiz to test or stretch their theory abilities, knowing that the types of questions and standards of wording are in keeping with what we'd like to see. Like Andy Wade I find that this kind of quiz makes me realise that there are some bits of theory that I could do with re-reading.
As for precison of wording, this is a perennial subject within BSAC and there's a raft of instructors who have _major_ issues on this topic. Terry H often (quite rightly) points out that just because BSAC is run in a "non-commercial" manner, this is no excuse for sloppy practice. This doesn't just apply to questions in the mag, the theory exams as supplied by HQ are frequently criticised by many who implement them.
The introduction of the new DTP is a positive sign that our organization isn't standing still, but there's a few more areas which could do with further attention, and I know several who agree with me that ambiguous questions and wordings, whether in a fun type quiz or in a diver grade examination, is one of THE major areas.
Regards
Steve W
PS: Mike, you've created a top quote there mate ;)
almost as good as Vic's "Continue your witterings in the crayon colour of your choice..."
Can I borrow it please? I think that could become very popular indeed :)))
BTW don't you think that if you have to argue the case for unambiquity then the question has already been answered?
Mike Halligan
20-03-2003, 14:18
"Totally unambiguous and has but two correct answers" - that's a classic, Mike!
The perils of drafting on the fly! I had intended to write that it would appear unambiguous to any given candidate but had two potentially correct answers. So long as the instructor is aware (and I wasn't, earlier today) this would be OK.
Mike ;-))
Mike Halligan
20-03-2003, 14:21
Mike, I hope this is in jest. If there are "but two correct answers", the question is ambiguous!
Nah! Simple confusion on re-writing.
;-))
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