I have a triangle. It is a right triangle. The only side that has a known length is the hypotenuse. The other two angles are known. How do I determine the legth of the other two sides without knowing the sine, cosine, or tangent; OR if these are nescesary, how do I determine them with only the knowledge of the angles?
>>3
I'm sure he does. If you're seriously asking, I'd like to know why you don't have a calculator to evaluate your trig functions.
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Anonymous2007-01-10 17:17
>>4
I am. And as for the caulculator, at the time I came across this problem I had no calculator. While I could easily solve it now with my computer calc I just want to know if it can be done.
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Anonymous2007-01-10 17:32
>>5
The purpose of the sin and cosine functions is to describe the relationship between the hypoteneuse and one of the other two sides. You can memorize a few values with simple fractional representations (I have 0, 30, 45, 60, and 90 for sine, and you can figure out their counterparts in each pi/2 interval after that and the same for cosine with that info), but without that ratio, you're boned. Also, it is hard to work with irrationals without a calculator.
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Anonymous2007-01-10 17:38
All you need is 3 data. 3 angles, 2 angles and 1 side, 2 sides and 1 angle, or 3 sides.
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Anonymous2007-01-10 18:42
>>7
gb2 grade school. There are an infinite number of similar right triangles for each valid set of angles. Then tell us how you can use the angles without their trig functions, dumbass.
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Anonymous2007-01-10 19:36
>>7
Also 1 angle/2 side (A-S-S LOL) does not necessarily determine a unique triangle.
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Anonymous2007-01-10 21:58
True. Only ASA.
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Anonymous2007-01-11 9:14
>>9
S-A-S would I dentify a unique triangle though.
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Anonymous2007-01-11 11:35
>>9
there is only SAS, ASA, SSS, and AAS, along with the definition of congruent triangles. gb2 high school there is no Angle-side-side
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Anonymous2007-01-11 11:39
>>12
That's exactly what he just said. gb2 grade school and learn to read.
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Anonymous2007-01-11 12:14
>>12
You sound like a middle schooler so anxious to show what you learned in class today, you don't even bother reading the posts you're replying to.
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Anonymous2007-01-11 16:45
Does anyone even remember the SAS ASS SSS all that crap except middle schoolers? If I wanted to know stuff about triangles, I would use the pythagorean theorem or look up the law of cosines.
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4tran2007-01-11 16:52
ASS determines a unique triangle if A = 90 degrees.
Else, 2 triangles are possible.
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Anonymous2007-01-11 17:36
>>15
If you understand it, you don't need to memorize it.
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Anonymous2007-01-11 19:28
>>16
A = 30 degrees, S_1 = 1, S_2 = 1/2 allows only one triangle.
Or, more generally, if S_2 = sin(A)*S_1 then a unique triangle is determined.
(Note: S_1 is the side attached to the angle A, S_2 is the side opposite from the angle A)
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4tran2007-01-11 19:42
good point, I stand corrected
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Anonymous2007-01-11 19:46
>>18
Doesn't that suggest that S_1 is the hypoteneuse and not the attached leg?
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Anonymous2007-01-11 21:36
>>20
It's both. Try and think for a second before posting.
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Anonymous2007-01-11 22:04
>>21
The hypoteneuse and the two legs are by definition three separate things. Try to be less arrogant before posting a dumb like that.
>>22
Jesus christ. The angle A isn't the right angle (note how 30 degrees != 90 degrees), and hence one of THAT ANGLE'S legs is the hypotenuse.
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Anonymous2007-01-12 9:57
>>22
If your using sine to determine if the length of the other leg is valid, then the first line MUST be the hypotenuse.
>>25
Given your agument alone it stands that the line you are refering to could be either. And note that if you are using the adjacent side that is NOT the hypotenuse you wouldn't be able to use sine. So if you are the one who posted >>21, and your argument is that you can use either side, you are incorrect in that statement.
What, you've never seen a line before? Sure, it looks like one measly line, and that can't be a triangle since a triangle has 3 sides, so it couldn't possibly be a triangle. Unless, of course, one of the angles approaches zero.
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Anonymous2007-01-12 13:35
>>26
If you select S_2 as described in my original post (in terms of S_1 and A), then S_1 MUST be the hypotenuse of the resulting triangle. There is no other possibility - if there was, it wouldn't UNIQUELY determine a triangle.
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Anonymous2007-01-12 15:08
>>25
Angles don't have legs. Triangles do. Read the Wikipedia article 'Leg (geometry)'.
>>27
A geometric shape is static and cannot 'approach' anything; furthermore, the meaning of the word 'approach' requires that it never reach zero, as it would have to make a line.
Also, in any valid triangle, each side is less than the sum of the other two. Tell me how a line satisfies this.
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Anonymous2007-01-12 15:17
>>29
Triangles have angles, and angles in a triangle have adjacent sides, which I have always heard called legs. Also, if you're going to take a jab at >>27 you may as well bring up that he is confusing lines with line segments.
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Anonymous2007-01-12 17:34
>>30
Then someone has been misusing the words. The legs are the two sides of a right triangle that meet to form the right angle; the terms 'adjacent' and 'opposite' each refer exclusively to one of these sides based on which of the other two angles you are focusing on.
Eh, there is no ambiguity. We all know what is meant by 'line' here.
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Anonymous2007-01-12 17:41
>>31
Yes, we all know he meant line segment, just as everyone past middle school knows what was meant by legs of an angle in a triangle. If you're going to be an irritating pedant, then either do it well or GTFO.
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Anonymous2007-01-12 18:54
>>32
Referring to the hypoteneuse as a leg, which it by definition is not, is different from referring to a line segment as a line, which is an omissive shorthand and becomes totally correct when you put the word 'segment' back in.
>>35
Oh and additionally, note the use of "generally", meaning "not in every case" you second-rate high school pedant.
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Anonymous2007-01-12 21:45
>>36
We are talking exclusively about right triangles here.
>>37
Of course you would jump on that one word. Nevermind that it exactly echoes what I said; it says 'generally'! That's the same as if it said 'only once in a while'!
"A leg of a triangle is one of its sides. For a right triangle, the term "leg" generally refers to a side other than the one opposite the right angle (which is termed the hypotenuse)."
Now, the very first sentence supports my use of the word leg. The second sentence says that IN THE CASE OF A RIGHT TRIANGLE, it GENERALLY refers to a side other than the hypotenuse. In other words, sometimes it DOES NOT function like this - much like how when I used it, it DID NOT function like that.
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Anonymous2007-01-12 23:55
>>39
Google 'leg right triangle'. The first two links give definitions that unambiguously agree with me. The third explains SAS with the word 'leg' in a usage that would be nonsensical and incorrect if it included the hypoteneuse in this definition. Also, Wikipedia agrees with me. There's nothing at stake here; just accept that you're wrong and move on.
>>40
My point was never that your definition isn't acceptable, or even that it isn't the most common. My point is that there IS ambiguity to it, unlike you claim. If one reasonable source supports my definition then I am correct in making that point.
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Anonymous2007-01-13 3:57
While you cunts are arguing about definition, there's a term I need help with. It's that math word that means defining a mathematical object using special cases of more complex constructs -- such as defining a line by calling a triangle with one side being of zero size. You know what I'm talking about....
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Anonymous2007-01-13 6:10
Not to inject any actual relevance, but it sounds like what the OP's asking for is "How do I determine sin theta or cos theta without a calculator?"
The short answer: have lots of free time, know what the values are for 30, 45, and 60 degrees, and use the double- or half-angle formulae. Alternately, use a Taylor series, but that sucks plenty as well.
>>52
not really. algebra 1 during either 8th grade or 9th grade.
but if you're really smart, you can start to learn in in 7th.
then, you take algebra 2 or geometry. geometry is required to graduate and algebra 2 isnt. you do need algebra 2 for Physics class though. after you take algebra 2 you are allowed to take calculus, and after that (or a letter of reccomendation from a teacher) you can do AP Calc. im looking at the fucking course book right now.
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Anonymous2007-01-15 20:20
>>53
and also you only need 3 math credits to graduate (obviously geometry is one of them). (one credit equals 1 year long class of 80 minutes)