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anonymous
 one year ago
Trig and triangles. Is this possible?
One sec, I am typing it up.
anonymous
 one year ago
Trig and triangles. Is this possible? One sec, I am typing it up.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, it stats that \( \large a\geq b\space and \space a>h =b * sin A \) there is one triangle Well I have a situation where a is greater than b and a is greater than h so there should be one triangle Well, using Sine Law, I get that there can be two angles for sine A, which should mean there are two triangles correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oo some one would have to be a pro to figure that out...

abb0t
 one year ago
Best ResponseYou've already chosen the best response.0Yes. Are there choices? I can give you the answer.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No choices. Let me see if I can make one up close to it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a =40, b =10 , B=5 degrees a and b are sides. Ok, If we do \( \large \frac{sin5}{10}=\frac{sin A}{40} = 20.40 \) Now the law states\( \large a\geq b\space and \space a>h =b * sin A \) But clearly we have another angle we can use for A. We can use 159.6, which should mean we have two triangles correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Astrophysics @math1234

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This has to do with Sine Law

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It has to do with Sine Law and figuring out if there is one or two triangles

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0height drawn from vertex A to its opposite base?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The rule stats that \( \huge \large a\geq b\space and \space a>h =b * sin A \) is one triange but Sine Law says different because I can use another angle for A.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I am drawing a picture

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1\(a\geq b\) and \(h = b sinA\) since BH is the height, we have sin A = h/c hence \(sinA = \dfrac{h}{c}=\dfrac{bsinA}{c}\), hence b =c

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435185224437:dw

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1But I am not sure what you want me to do. hehehe....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a =40, b =10 , B=5 degrees Well, the rule states \( \large a\geq b\space and \space a>h =b * sin A \) a is greater than b and a is greater than h so we should have one triangle. Ok, but now Sine Law goes \(\large A=\frac{sin5}{10}=\frac{sin A}{40} = 20.40 \) h = 10* sin(20.40) =3.42 So a is greater than h but we can use another angle since 18020.40 = 159.6 and B only = 5 so 159.6+ 5 = 169.6 so C can equal 10.4 if we use angle 159.6. But this shows we have two triangles using sine law correct but the other rule must not hold true?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.015 owlbucks to help me understand. To me it seems the rule(\( \large (a\geq b\space and \space a>h =b * sin A ) \) = one triangle) does not hold true.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0In my studies this is call the Ambiguous Case of (SSA) Side Side Angle

phi
 one year ago
Best ResponseYou've already chosen the best response.3I think they are using the rule to differentiate between these two triangles: dw:1435187302571:dw

phi
 one year ago
Best ResponseYou've already chosen the best response.3just using the law of sines allows both the obtuse triangle (with short a) and acute triangle with long a for the obtuse triangle, b sin theta is bigger than side a

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This is what they stat When two sides and an angle are given, the resulting information may result in one triangle, two triangles or no triangle at all, depending on the relationship between a, h, b. No Triangle = a<h=b sinA One Right Triangle = a = h =b sinA Two Triangles = b>a>h=b sinA One Triangle a >=b and a> h=b sinA

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0With the triangle I have up there, these rules do not hold true.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Am I right? Those rules I have do not apply correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now they apply to one of the examples they give with the rules, which is a=7, b=5 A=70

phi
 one year ago
Best ResponseYou've already chosen the best response.3I think we have to be clear what side is a and b. Your example a =40, b =10 , B=5 degrees has only one triangle for a solution, so the "rule" should work, as long as we are careful about the definitions

phi
 one year ago
Best ResponseYou've already chosen the best response.3when they say "2 sides and an angle" do they mean the "included angle" ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, that is how I take it.

phi
 one year ago
Best ResponseYou've already chosen the best response.3for this to work One Right Triangle = a = h =b sinA it means side b is the hypotenuse and angle A is opposite side a dw:1435188557398:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What gets me is that if sinA = 20.40 that means there is another Angle for A correct? Because they 18020.40 = A =159.6 also? But this could be where I am guffing and thinking there could be two triangles. I might need to draw it out with angle 159.6

phi
 one year ago
Best ResponseYou've already chosen the best response.3Looking at your rules (trying to make sense of them) No Triangle = a<h=b sinA means dw:1435188767810:dw

phi
 one year ago
Best ResponseYou've already chosen the best response.3so the first two make sense. But note the angle is *not* the included angle between a and b

phi
 one year ago
Best ResponseYou've already chosen the best response.3One Triangle a >=b and a> h=b sinA I think your example that you entered up above fits this one.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The rules make sense but it is when I start using Sine Law and when I got A= 20.40 and then there can be another angle for A, which is 18020.40 = A = 159.6

phi
 one year ago
Best ResponseYou've already chosen the best response.3and this one Two Triangles = b>a>h=b sinA means dw:1435189157259:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0A could = 159.6 because b=5 so 18020.40 = 159.6+5 = 164.6 and C could = 180164.6 = 15.4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But I have not drawn out the triangle to see what it looks like

phi
 one year ago
Best ResponseYou've already chosen the best response.3maybe this is the problem the rule uses 2 adjacent sides a and b, and the angle *opposite side a* (so which angle we know defines side a, and b by default is the the other given side)

phi
 one year ago
Best ResponseYou've already chosen the best response.3Thus in your example: a =40, b =10 , B=5 degrees we then label it this way: The angle is always A: angle A= 5 side a= 10, side b= 40 now it looks like we use this rule Two Triangles = b>a>h=b sinA and you are correct, we do get two triangles

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok I am perplexed. On the problem I posted do the rules hold true? I am given the problem as B=5 not A = 5. but it appear this triangle has two and not 1.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I have to find A before the rules work.

phi
 one year ago
Best ResponseYou've already chosen the best response.3The rules require you to label the sides and angle in a very specific way. There is no choice: the angle must be labeled A, and the side opposite angle A is side a and the remaining side becomes b. Now you can use the rule.

phi
 one year ago
Best ResponseYou've already chosen the best response.3If you are given 2 sides and an angle that is *not included between them* label the given angle A (no matter what the problem calls it) label its opposite side a label the remaining side b now you can use the rule.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Since they are using A but I have B the rule for me b>=a and b> h =sinB

phi
 one year ago
Best ResponseYou've already chosen the best response.3Here is trying to make 2 triangles with a=40 and b=10

phi
 one year ago
Best ResponseYou've already chosen the best response.3Here is the other way round, b=40, a=10 now we can make two triangles (see the red and blue lines)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, we can create two triangles but I am wondering about the rules.

phi
 one year ago
Best ResponseYou've already chosen the best response.3What is a problem you want to analyze using the rules?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435191754375:dw To me it seems the rule is being applied like b >= a and b> h=a sinB

phi
 one year ago
Best ResponseYou've already chosen the best response.3ok. In that picture, to use the rule you must rename it (as we have already discussed) then when you apply the rule, you will find two triangles are possible.

phi
 one year ago
Best ResponseYou've already chosen the best response.3i.e A = 5, B is unknown , side a=10 , side b= 40

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It is holding true how I have it right?? b= 10 a = 40 and B =5 No Triangle = b<h=a sinB One Right Triangle = b = h =a sinB Two Triangles = a>b>h=a sinB One Triangle b >=a and b> h=a sinB

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sine Law showed me there was two triangle but I was setting up the rule above wrong because that is how they explain it but actually it can be set up like I just did correct?

phi
 one year ago
Best ResponseYou've already chosen the best response.3yes, you can relabel in the rules. But the idea is to be consistent.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, I see what I was doing wrong. It is how I was setting up the rules I just posted. I knew there was two triangles thanks to Sine Law but I was confused on the rules because the way the explained it and made it seem like that I had to use b and SineA but I can use a sinB long as it is the same pattern

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I sent you 20 owlbucks. Thank once again.
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