I'm not sure on what to do | Mathematics | Page 1

idle chasm May 21, 2024, 4:40 PM

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I've heard I should use Stewart's Theorem, but I'm not sure if thats correct or how to apply it

gritty dirgeBOT May 21, 2024, 4:40 PM

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idle chasm I've heard I should use Stewart's Theorem, but I'm not sure if thats correct or ...

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tame widget May 21, 2024, 4:41 PM

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idle chasm I've heard I should use Stewart's Theorem, but I'm not sure if thats correct or ...

What does Stewart's theorem state?

idle chasm May 21, 2024, 4:42 PM

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tame widget What does Stewart's theorem state?

tame widget May 21, 2024, 4:42 PM

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idle chasm

So to use it, you just need to define a, b, c, d, m, and n, right?

idle chasm May 21, 2024, 4:43 PM

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tame widget So to use it, you just need to define a, b, c, d, m, and n, right?

Well Im guessing I gotta use what I know to find the ones I dont

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But Im not sure how

tame widget May 21, 2024, 4:44 PM

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idle chasm Well Im guessing I gotta use what I know to find the ones I dont

...yes, and to do that you first need to identify what in this problem a, b, c, d, m, and n are.

idle chasm May 21, 2024, 4:45 PM

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well c = 12 , b = 15 and d = 10

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but idk the other 3

tame widget May 21, 2024, 4:46 PM

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You know more than you think.

tame widget May 21, 2024, 4:46 PM

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idle chasm

What's the relationship in this diagram between m, n, and a?

idle chasm May 21, 2024, 4:47 PM

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m+n=a

tame widget May 21, 2024, 4:47 PM

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idle chasm I've heard I should use Stewart's Theorem, but I'm not sure if thats correct or ...

And what's stated here about AD?

idle chasm May 21, 2024, 4:47 PM

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That it's 10cm

tame widget May 21, 2024, 4:47 PM

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And?

idle chasm May 21, 2024, 4:48 PM

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its a bisector

tame widget May 21, 2024, 4:48 PM

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Which means what?

idle chasm May 21, 2024, 4:48 PM

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It splits the angle into 2 equal ones

tame widget May 21, 2024, 4:48 PM

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Does it bisect angle A, or does it bisect side BC?

idle chasm May 21, 2024, 4:48 PM

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angle A

tame widget May 21, 2024, 4:49 PM

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You sure?

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It seems ambiguous to me.

idle chasm May 21, 2024, 4:49 PM

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Yeah

tame widget May 21, 2024, 4:49 PM

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And I don't see how we can directly apply Stewart's theorem if that is the case.

idle chasm May 21, 2024, 4:49 PM

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tame widget You sure?

Maybe translation error on my part

tame widget May 21, 2024, 4:50 PM

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Translation? It's in English.

idle chasm May 21, 2024, 4:50 PM

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It was in a diff language but I translated it

tame widget May 21, 2024, 4:50 PM

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Okay.

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So the original problem specified AD was an angle bisector?

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Because that means we probably have to use trigonometry.

idle chasm May 21, 2024, 4:51 PM

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tame widget So the original problem specified AD was an *angle* bisector?

yeah

tame widget May 21, 2024, 4:53 PM

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See, because if AD bisected BC, that would make m = n, so we could invoke Stewart's theorem with only one unknown.

idle chasm May 21, 2024, 4:54 PM

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yeah i know it would be much easier then

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but sadly that's not the case

tame widget May 21, 2024, 4:54 PM

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As it is I'm actually not sure how Stewart's theorem is applicable at all.

idle chasm May 21, 2024, 4:55 PM

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I'm not sure what to do or what formulas to use

tame widget May 21, 2024, 4:55 PM

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Like I said, if it bisects the angle, that means we have to use trigonometry.

idle chasm May 21, 2024, 4:55 PM

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cosinus theorem?

tame widget May 21, 2024, 4:56 PM

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Law of cosines seems the most straightforward method, yeah.

idle chasm May 21, 2024, 4:56 PM

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but we don't know the angle though

tame widget May 21, 2024, 4:57 PM

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I don't think we have to. We know a = m + n, and we know the only two angles involved are A and A/2.

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Was it your teacher who said to use Stewart's theorem, or a fellow student, or who?

idle chasm May 21, 2024, 4:59 PM

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I saw it on ChatGPT actually

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and it gave the correct answer

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but the method was weird

tame widget May 21, 2024, 5:00 PM

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Ugh, ChatGPT.

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Here's the thing about ChatGPT.

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It's not good at math.

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It doesn't know math at all.

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All it knows is how to put one word after another.

idle chasm May 21, 2024, 5:01 PM

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It did get it right though

tame widget May 21, 2024, 5:01 PM

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It actually started outsourcing math processing to WolframAlpha a while back, but that's still dependent on it recognizing the math problem well enough to invoke the subroutine.

idle chasm May 21, 2024, 5:01 PM

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surprisingly

tame widget May 21, 2024, 5:02 PM

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And the information it passes to WA about the problem is dependent on what information ChatGPT can recognize as being about the problem.

idle chasm May 21, 2024, 5:04 PM

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So , as for the problem, any ideas on how to actually solve it? 😅

tame widget May 21, 2024, 5:04 PM

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Basically, the best case scenario of asking ChatGPT a math question is that you're actually just asking WolframAlpha a math question.

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The worst case scenario is that ChatGPT asks WolframAlpha a garbled version of your question because either you or it weren't specific enough.

tame widget May 21, 2024, 5:05 PM

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idle chasm So , as for the problem, any ideas on how to actually solve it? 😅

Like I said, law of cosines seems applicable.

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It reduces the three unknowns to the one unknown of angle A.

idle chasm May 21, 2024, 5:07 PM

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but we only know 2 sides from any triangle, so how can we apply cosinus theorem?

tame widget May 21, 2024, 5:07 PM

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...that's like asking how we can apply the Pythagorean theorem if we only know two sides.

idle chasm May 21, 2024, 5:08 PM

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dont we need an angle or the opposing side of the angle?

tame widget May 21, 2024, 5:08 PM

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What did I say? We're reducing three unknowns to one.

idle chasm May 21, 2024, 5:08 PM

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I feel stupid rn

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I dont get it

tame widget May 21, 2024, 5:08 PM

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Okay.

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a = m + n.

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If a = f(A), m = g(A), and n = h(A), then we have f(A) = g(A) + h(A). Everything depends on A.

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We find A, we find everything.

idle chasm May 21, 2024, 5:10 PM

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Is f(A) a function or something?

tame widget May 21, 2024, 5:10 PM

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Yes. It's expressing the length of side a as a function of angle A.

idle chasm May 21, 2024, 5:11 PM

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This is even more confusing

tame widget May 21, 2024, 5:11 PM

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Look, let's just go with it for now. If we want the law of cosines with angle A, what do we get?

idle chasm May 21, 2024, 5:13 PM

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a^(2)=144+225-360*cos(A)

tame widget May 21, 2024, 5:13 PM

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Right. Which means a = sqrt(369 - 360cos(A)), right?

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So now what does m equal according to the law of cosines?

idle chasm May 21, 2024, 5:15 PM

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well m is a part of a so

tame widget May 21, 2024, 5:15 PM

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In its own triangle.

idle chasm May 21, 2024, 5:15 PM

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m+n=sqrt(369 - 360cos(A)) ?

tame widget May 21, 2024, 5:16 PM

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No. In triangle ABD.

idle chasm May 21, 2024, 5:17 PM

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tame widget No. In triangle ABD.

m= sqrt(325-300cos(A/2) )

tame widget May 21, 2024, 5:17 PM

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And in triangle ACD, what's n?

idle chasm May 21, 2024, 5:19 PM

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n = sqrt( 244-240cos(A/2) )

tame widget May 21, 2024, 5:20 PM

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Therefore, $a = m + n$, so $\sqrt{369 - 360\cos{A}} = \sqrt{325 - 300\cos{\frac{A}{2}}} + \sqrt{244 - 240\cos{\frac{A}{2}}}$, right?

full plumeBOT May 21, 2024, 5:20 PM

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Techie Literate

idle chasm May 21, 2024, 5:21 PM

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yeah

tame widget May 21, 2024, 5:21 PM

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And notice that the only variable in this equation is A.

idle chasm May 21, 2024, 5:21 PM

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Yeah

tame widget May 21, 2024, 5:22 PM

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Which means this equation is (in principle) solvable for A, especially considering we know 0 < A < 180, and once we've solved for A we can plug that value into the law of cosines for a.

idle chasm May 21, 2024, 5:23 PM

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Okay but how can we find A?

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Because that thing looks horrible to solve

tame widget May 21, 2024, 5:23 PM

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Oh, it's long and annoying, but it's all relatively basic algebra.

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Square both sides, isolate the remaining square root term, square both sides again.

idle chasm May 21, 2024, 5:24 PM

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if we square both sides we will get a montrosity

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so idk

tame widget May 21, 2024, 5:24 PM

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And invoke the double angle identity on cos(A) to make it purely a polynomial in cos(A/2).

tame widget May 21, 2024, 5:25 PM

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idle chasm if we square both sides we will get a montrosity

Like I said, long and annoying, but not really a technical challenge, just a test of patience and attention to detail.

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In fact.

idle chasm May 21, 2024, 5:25 PM

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did u solve it and got a proper answer?

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or some weird thing

tame widget May 21, 2024, 5:26 PM

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,w solve sqrt(369 - 360cos(A)) = sqrt(325 - 300cos(A/2)) + sqrt(244 - 240cos(A/2)),

full plumeBOT May 21, 2024, 5:26 PM

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Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

idle chasm May 21, 2024, 5:26 PM

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bruh

tame widget May 21, 2024, 5:26 PM

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That's what WolframAlpha is for. It can't solve word problems, but it can certainly solve equations.

idle chasm May 21, 2024, 5:27 PM

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i feel like something is wrong

tame widget May 21, 2024, 5:27 PM

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Why?

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I mean, it might be able to solve word problems if it could parse them, but that's a big if. It's not a language machine.

tame widget May 21, 2024, 5:31 PM

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idle chasm i feel like something is wrong

Seriously, though, what's wrong?

idle chasm May 21, 2024, 5:33 PM

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Well the sheet that has the answer also has some steps on how to solve
it says you're supposed to get
144+100-240cos(A)=16k^(2)
and
225+100-300cos(A)=25k^(2)

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but idk how it got them

idle chasm May 21, 2024, 5:34 PM

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tame widget Seriously, though, what's wrong?

perhaps we did something wrong

tame widget May 21, 2024, 5:36 PM

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If you have an answer sheet, why don't you just show me that and I'll explain that method?

idle chasm May 21, 2024, 5:39 PM

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Alr lemme translate it rq

idle chasm May 21, 2024, 5:42 PM

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tame widget If you have an answer sheet, why don't you just show me that and I'll explain th...

Here

tame widget May 21, 2024, 5:46 PM

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idle chasm Here

Okay, clearly they're saying BD/DC = 4/5, but I don't know what justifies that ratio.

idle chasm May 21, 2024, 5:50 PM

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tame widget Okay, clearly they're saying BD/DC = 4/5, but I don't know what justifies that r...

This probably

tame widget May 21, 2024, 5:51 PM

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Ah. Well then yeah.

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Then it's just a straightforward application of the law of cosines.

idle chasm May 21, 2024, 5:53 PM

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yeah but how is k=2?

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I dont get how u solve those

tame widget May 21, 2024, 5:55 PM

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It's just simultaneous equations

tame widget May 21, 2024, 5:56 PM

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idle chasm Here

Multiply the first equation by 300/240, then subtract it from the second equation.

idle chasm May 21, 2024, 5:59 PM

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tame widget Multiply the first equation by 300/240, then subtract it from the second equatio...

dont we have to multiply both?

tame widget May 21, 2024, 5:59 PM

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Why?

idle chasm May 21, 2024, 5:59 PM

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well then they wont really be equal anymore

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or related

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Like what stops us from multiplying the first one by 100 and leaving the second one as it is

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it will completely change it

tame widget May 21, 2024, 6:00 PM

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No it won't.

tame widget May 21, 2024, 6:00 PM

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idle chasm or related

They aren't related.

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Apart from having the same two variables in them.

idle chasm May 21, 2024, 6:03 PM

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Alright it gave me that k=2 just like there

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nice

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well thank you for the help

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Salute

#I'm not sure on what to do