Need help! | Mathematics | Page 1

urban pike Apr 15, 2024, 10:23 PM

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wooden lotusBOT Apr 15, 2024, 10:23 PM

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urban pike

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balmy sorrel Apr 15, 2024, 10:25 PM

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urban pike

What's the original problem?

urban pike Apr 15, 2024, 10:25 PM

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Let me translate it rq.

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In ABC triangle AD:BD = 3:2, AE:EC = 1:3. Find ADE triangle's area divided to ABC triangle's area.

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Hopefully I made it understandable

balmy sorrel Apr 15, 2024, 10:27 PM

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...wait, what's D and E?

urban pike Apr 15, 2024, 10:27 PM

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This one

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balmy sorrel Apr 15, 2024, 10:28 PM

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...okay, but does the problem explicitly state that D is on AB and E is on AC?

urban pike Apr 15, 2024, 10:28 PM

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Not really.

balmy sorrel Apr 15, 2024, 10:28 PM

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Then they could be anywhere.

urban pike Apr 15, 2024, 10:28 PM

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True

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Would you like me to

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Send possible answers?

balmy sorrel Apr 15, 2024, 10:30 PM

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Oh, it's multiple choice?

urban pike Apr 15, 2024, 10:30 PM

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No, there's only one possible answer

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There's just 4 here listed in which one of em could be the correct one

balmy sorrel Apr 15, 2024, 10:30 PM

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...right, so then there's four possible answers.

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One of which is the actual answer.

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You're just describing a multiple-choice problem.

urban pike Apr 15, 2024, 10:31 PM

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Yeah

balmy sorrel Apr 15, 2024, 10:31 PM

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So the answer to "Oh, it's multiple choice?" is "Yes."

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Hmm.

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Okay, so actually I think there's an easier way to do this.

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First of all, we can just declare ABC is a right triangle.

urban pike Apr 15, 2024, 10:32 PM

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Okay

balmy sorrel Apr 15, 2024, 10:32 PM

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That simplifies our lives a lot because it simplifies how we represent the area of ABC.

urban pike Apr 15, 2024, 10:32 PM

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But dont ADE and ABC share one corner already?

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Actually scratch my question

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Continue

balmy sorrel Apr 15, 2024, 10:33 PM

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Okay. So ABC is a right triangle, and just to keep with tradition let's make C the right angle.

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Hypothetically, I think it's possible for ADE to also be a right triangle.

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Specifically if E is on AC and D is directly above E.

urban pike Apr 15, 2024, 10:34 PM

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It isn't on the drawing here

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balmy sorrel Apr 15, 2024, 10:35 PM

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I didn't know that was actually an official drawing.

urban pike Apr 15, 2024, 10:35 PM

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My bad for that one

balmy sorrel Apr 15, 2024, 10:35 PM

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It looked like just your drawing of the situation, which is why I asked if the question explicitly stated D was on AB and E was on AC.

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And it does, apparently, in the provided figure.

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Look.

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Just give me the whole question.

urban pike Apr 15, 2024, 10:36 PM

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It's entirely in a different language

balmy sorrel Apr 15, 2024, 10:36 PM

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I don't care. I'll ask for translations of things I need translated.

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But I can't work without all of the necessary information.

urban pike Apr 15, 2024, 10:37 PM

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It's the fifth one

balmy sorrel Apr 15, 2024, 10:38 PM

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Okay, so we're looking for the area of ADE as a fraction of the area of ABC, right?

urban pike Apr 15, 2024, 10:38 PM

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It's georgian

balmy sorrel Apr 15, 2024, 10:38 PM

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That is, area(ADE)/area(ABC)?

urban pike Apr 15, 2024, 10:38 PM

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Yeah

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Correct

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Area (ADE) / area(ABC)

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That's what we have to find

balmy sorrel Apr 15, 2024, 10:38 PM

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Okay, so.

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Wait, holy shit, we've been overthinking this.

urban pike Apr 15, 2024, 10:39 PM

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What?

balmy sorrel Apr 15, 2024, 10:39 PM

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What's the formula for the area of a triangle?

urban pike Apr 15, 2024, 10:39 PM

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It's

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S = h * a

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A being the

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Base

balmy sorrel Apr 15, 2024, 10:39 PM

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...no.

urban pike Apr 15, 2024, 10:39 PM

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Wait

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S = a * h / 2

balmy sorrel Apr 15, 2024, 10:40 PM

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Right.

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So what's the base of ABC?

urban pike Apr 15, 2024, 10:40 PM

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It's 4x

balmy sorrel Apr 15, 2024, 10:40 PM

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Well, no, not necessarily.

urban pike Apr 15, 2024, 10:40 PM

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Just 4 then

balmy sorrel Apr 15, 2024, 10:41 PM

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Okay, that works.

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So now what's the height?

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Actually, wait, that doesn't work.

urban pike Apr 15, 2024, 10:41 PM

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We don't know but we can use a formula for thay one right?

balmy sorrel Apr 15, 2024, 10:41 PM

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The problem is.

urban pike Apr 15, 2024, 10:41 PM

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Ok

balmy sorrel Apr 15, 2024, 10:41 PM

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We have the ratios the points split the sides into.

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But we don't know the ratios have the same common factor.

urban pike Apr 15, 2024, 10:42 PM

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Ahuh

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3/20 is the correct answer btw

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I checked

balmy sorrel Apr 15, 2024, 10:43 PM

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Okay, look, here's how it works.

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The base of triangle ABC is AC.

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So what's the height?

urban pike Apr 15, 2024, 10:44 PM

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We don't know..

balmy sorrel Apr 15, 2024, 10:44 PM

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...we can figure it out.

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Draw in the height.

urban pike Apr 15, 2024, 10:48 PM

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Let's try a different approach, let's say AB is a and BC is b.

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AD = 3/5 * a

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BD = 2/5 * a

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AE = 1/4 * b

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And EC = 3/4 * b

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We gotta find the areas of the triangles so

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Area of ADE is

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1/2 * AD * AE

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Hm

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1/2(3/5a)(1/4b)

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For ade area

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Which is

balmy sorrel Apr 15, 2024, 10:53 PM

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urban pike

So looking here, what's the height?

urban pike Apr 15, 2024, 10:53 PM

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Dunno

balmy sorrel Apr 15, 2024, 10:53 PM

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urban pike 1/2 * AD * AE

Wait, how does that follow?

urban pike Apr 15, 2024, 10:53 PM

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I don't think that's relevant hols on

balmy sorrel Apr 15, 2024, 10:53 PM

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urban pike I don't think that's relevant hols on

It's relevant.

urban pike Apr 15, 2024, 10:53 PM

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balmy sorrel Wait, how does that follow?

Oh

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Fuck yeah you're right

balmy sorrel Apr 15, 2024, 10:54 PM

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Look, have you studied trigonometry?

urban pike Apr 15, 2024, 10:54 PM

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Not yet.

balmy sorrel Apr 15, 2024, 10:54 PM

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Okay.

urban pike Apr 15, 2024, 10:54 PM

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We will soon though

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Anyway back to the topic

balmy sorrel Apr 15, 2024, 10:55 PM

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I actually am not totally sure how you're supposed to do this without trig.

urban pike Apr 15, 2024, 10:56 PM

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Hm.

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I'll just abandon it

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Mark it and get back to it later

balmy sorrel Apr 15, 2024, 10:57 PM

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With trig it's dead simple, though.

urban pike Apr 15, 2024, 10:57 PM

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You're free to explain it

balmy sorrel Apr 15, 2024, 10:59 PM

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Okay, so I don't know how this acronym will translate into your language, but a mnemonic we use for trig in English is SOHCAHTOA, which stands for sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent.

urban pike Apr 15, 2024, 11:00 PM

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Okay continue

balmy sorrel Apr 15, 2024, 11:00 PM

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The way it works is, if you have a right triangle, and one of the non-right angles has measure T, then these trigonometric functions evaluated at T equal those ratios of sides in the triangle.

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In this case, the "adjacent" side to the angle is the non-hypotenuse side which forms one leg of the angle, and the "opposite" side is the side which doesn't include the angle's endpoint. I'll draw you a picture when I can.

urban pike Apr 15, 2024, 11:05 PM

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Oh

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Wish this was correct though

balmy sorrel Apr 15, 2024, 11:11 PM

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urban pike Apr 15, 2024, 11:12 PM

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OHHHHHHH

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WE WENT OVER THAT ALREADY

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TRIGONOMETRIC RATIOS

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Yeah we did get over this already

balmy sorrel Apr 15, 2024, 11:12 PM

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Okay then.

balmy sorrel Apr 15, 2024, 11:13 PM

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urban pike

So then, looking back here, what can we say about the height of ABC?

urban pike Apr 15, 2024, 11:14 PM

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From the right angle right

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Sin 90 = 5x / AK

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Or if we're talking the other way sin 90 = BC / KC

balmy sorrel Apr 15, 2024, 11:15 PM

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...no.

urban pike Apr 15, 2024, 11:15 PM

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Fuck

balmy sorrel Apr 15, 2024, 11:16 PM

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What angle would be most useful here?

urban pike Apr 15, 2024, 11:16 PM

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The right angle?

balmy sorrel Apr 15, 2024, 11:16 PM

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...no.

urban pike Apr 15, 2024, 11:16 PM

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90 degree one?

balmy sorrel Apr 15, 2024, 11:16 PM

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What angle is in both our triangles?

urban pike Apr 15, 2024, 11:16 PM

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DAE?

balmy sorrel Apr 15, 2024, 11:17 PM

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...angle A, yes.

urban pike Apr 15, 2024, 11:17 PM

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Yeah

balmy sorrel Apr 15, 2024, 11:17 PM

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So what's sin(A)?

urban pike Apr 15, 2024, 11:17 PM

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Sin ( A) = h/5x

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Or Sin (A) = DE / 3x

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Mb

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Sin (A) = 3x/x

balmy sorrel Apr 15, 2024, 11:20 PM

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...no.

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Look, forget about x.

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x was a mistake, remember?

urban pike Apr 15, 2024, 11:20 PM

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Okay

balmy sorrel Apr 15, 2024, 11:20 PM

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sin(A) = h/AB.

urban pike Apr 15, 2024, 11:20 PM

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Got it

balmy sorrel Apr 15, 2024, 11:20 PM

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Therefore h = ?

urban pike Apr 15, 2024, 11:21 PM

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h = AB..?

balmy sorrel Apr 15, 2024, 11:21 PM

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...no.

urban pike Apr 15, 2024, 11:21 PM

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h = AB * Sin(A)

balmy sorrel Apr 15, 2024, 11:21 PM

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Yes.

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Why wasn't that the first thing you said?

urban pike Apr 15, 2024, 11:21 PM

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A typo

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Definitely a typo

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Was gonna say the second thing

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Anyway we found out that h = AB * Sin (A)

balmy sorrel Apr 15, 2024, 11:22 PM

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Right.

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Therefore the total area is what?

urban pike Apr 15, 2024, 11:23 PM

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S = AC * AB * Sin(A) /2

balmy sorrel Apr 15, 2024, 11:23 PM

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Right. And now onto ADE.

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What's the base?

urban pike Apr 15, 2024, 11:23 PM

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AE

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Right..?

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Wait

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No

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AD

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its AD

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AD is the base

balmy sorrel Apr 15, 2024, 11:24 PM

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...no, it's AE.

urban pike Apr 15, 2024, 11:24 PM

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Alr, AE

balmy sorrel Apr 15, 2024, 11:24 PM

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You seem more confused now than when we started. Are you okay?

urban pike Apr 15, 2024, 11:24 PM

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I am fine,

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AE is the base so

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I'm guessing the area is

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S = AE * AD * Sin(A) / 2

balmy sorrel Apr 15, 2024, 11:26 PM

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Right.

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So then just divide that by the first area we got.

urban pike Apr 15, 2024, 11:26 PM

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Got it

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Let me write it down real quick

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Is this correct?

balmy sorrel Apr 15, 2024, 11:29 PM

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Yes.

urban pike Apr 15, 2024, 11:29 PM

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Great!

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So

balmy sorrel Apr 15, 2024, 11:30 PM

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Wait ,no.

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Wrong way around.

urban pike Apr 15, 2024, 11:30 PM

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?

balmy sorrel Apr 15, 2024, 11:30 PM

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The top should be the bottom.

urban pike Apr 15, 2024, 11:30 PM

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Done

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Now we just

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Wait what would AE be?

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Since we aren't using x

balmy sorrel Apr 15, 2024, 11:32 PM

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Let's just do what we can before dealing with that for now.

urban pike Apr 15, 2024, 11:33 PM

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Done.

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It's 3/20

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Anyway

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Thank you techie for

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Everything

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For having the nerves of steel lol

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You're a savior

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+close

#Need help!