#1
Yeah, I have a couple of problems for my math class that I just dont understand at all. So, I was wondering if someone could possibly help me with them? Yes, I want the answers but more importantly I want to understand how to find the answer as well. And no, im not ashamed or embarresed for asking math help on a guitar forum, I believe you can find many interesting and good people on the internet, and this sort of forum can be used for many topics. Here's the problems (23-26):



I really could use some help.
Thanks much.
#2
Well, you have to find out the scale factor between the 2 triangles to find out the length of the vertical leg of triangle, ABC then use the pathagorian therum (sp?) and the law of sines/cosines to find out the rest of the information. I don't remember the formulas right now, but if you have them, you can just plug in the information you know.

Kind of breif, but I hope it helps.
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#3
Yeah, see I have no idea how to find the scale factor, and there really isn't a formula. My book isnt really helping me, or at least im just not getting it.

I know this all fairly simple, and revolves around algebra.
#4
I'll give it a go:

23. Scale factor means how much bigger/smaller one shape is than another congruent shape. The formula for working it out is

new length/old length

So you know BC and EF, just divide one by the other.

19.8/9= 2.2


24. Ok, well in the smaller triangle you chop it in half to get a triangle with side lengths 8(we'll call this B), 9(we'll call this A) and an unknown(we'll call this C). Then use Pythagoras' theorem, which says that the length of the hypotenuse(longest side) squared is equal to the lengths of the other two sides squared and added.

a squared= b squared + c squared

So we know A is 9, and B is 8. We want to find out C, so we'll rearrange the equation into the form:

c squared=a squared-b squared

Now put the numbers in:

c squared=9 squared-8 squared

c squared=81-64

c squared=17

c=4.123 to three decimal places

So now we know that C is 4.123. We can now concentrate on the other side of the triangle which actually has the length we need to know. We can take 4.123 from 10.4 to find the base length, so that's 6.277. Now just use Pythagoras again:

DE squared= 8 squared+6.277 squared

(working as before)

DE= 10.169

Handily, because we know the scale factor we can just multiply 10.4 by 2.2 to find AC.

AC= 22.88

25. I'm not sure what they mean by altitude(crazy American terminology ), but I'm guessing its just the height. If so, all we have to do is multiply 8 by 2.2, and voila.

8*2.2= 17.6

26. The formula for area of a triangle is:

0.5 multiplied by the base multiplied by the height(or 0.5*base*height)

So, for the smaller triangle:

0.5*10.4*8=41.6

Bigger triangle:

0.5*22.8*17.6=200.64


I've probably made a lot of mistakes there cause I'm doing it fast and I'm too lazy to check, but ah well someone cleverer than me will pick them up

Hope I helped
#5
Its pretty simple. But I am really not in the mood for maths. So other people can do it instead.
#6
scale factor = 19.8 / 9

so basically whatever length yoru asked for you find the corresponding length on the other triangle, if you want to make it bigger you *, smaller you /, simple.
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#7
Ahh, I owe you guys one. Thats fantastic.

Thanks all, much.



Quick question, with the Pythagorean Theorem part, are you supposed to take A squared minus B squared to get C squared? I thought you added the two? Or maybe for this certain situation?
Last edited by WyldeGibsonPlyr at Mar 19, 2007,
#9
Yeah, thats what I thought.
Just trying to figure out if maybe thats the way it was supposed to be done for that problem though.
#10
Well, if you want to be fancy:

c^2 = a^2 + b^2 + 2ab*cos(c)
(^Full equation)

That is the full Pythagorean Theorum. But since the cosine of C in most cases you use in geometry is 90 degrees, that makes the 2ab*cos(c) part drop out (cos(90)=0).

Come to think of it, whoever did this problem fucked it up bad.

You can't use the Pythagorean Theorum on these triangles without finding some angle measures, which is just a complete waste of time.

The scale factor is what you use to find all the sides:

- 19.8 / 9 = 2.2 (This is the ratio of 2 sides in the triangle)

Now you use this scale factor in the ratio of the other sides. Let's find side DE now:

22 / x = 2.2 -> Multiply both sides by X:
22 = 2.2x -> Divide both sides by 2.2:
x = 10 -> The side length DE = 10.

Now let's find side length AC:

x / 10.4 = 2.2 -> Multiply both sides by 10.4:
x= 22.88 -> The side length AC = 22.88.

The altitude part was right up above: 17.6

So now we find the areas of both triangles:

SM: 0.5*10.4*8 = 41.6
LG: 0.5*22.88*17.6 = 201.344

Now to compare the areas, all we do is divide the larger area by the smaller area:

201.344 / 41.6 = 4.84 -> The area of the larger triangle is 4.84 times larger than the area of the smaller triangle.

Now hopefully you check this out before you go to school, lol.
- FJ

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Last edited by flyingjew34 at Mar 20, 2007,
#11
Quote by flyingjew34

c^2 = a^2 + b^2 + 2ab*cos(c)
(^Full equation)


it's actually c^2 = a^2 + b^2 - 2ab*cosC, which is the cosine rule for sides, not the pythagorean theorem (a^2 = b^2 + c^2 where a is the hypotenuse)
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#12
Quote by The Overlord
it's actually c^2 = a^2 + b^2 - 2ab*cosC, which is the cosine rule for sides, not the pythagorean theorem (a^2 = b^2 + c^2 where a is the hypotenuse)

Ok, forgot it's minus. But that is essentially the full Pythagorean Theorum. Yes, it may be called the Law of Cosines, but if all Pythagorus did was take that theorum, drop out part of it, and make a new one, sounds pretty lame to me, lol.
- FJ

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#13
to make it easier, the scale factor would be 1:2.2. so, you would plug in all the lengths you didn't know as an equation, so 1 over 2.2 equals , say, x over 22. repeat for all the side lengths.

for the last one, you square the scale factor to find the area factor, so it would be 1:4.84. and area of a triangle is 1/2base*height.
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#14
Quote by flyingjew34
Ok, forgot it's minus. But that is essentially the full Pythagorean Theorum. Yes, it may be called the Law of Cosines, but if all Pythagorus did was take that theorum, drop out part of it, and make a new one, sounds pretty lame to me, lol.


actually im pretty sure you use pyhtagorous theorem to derive the cosine rule.......
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#15
Just another quick question (thanks for all the help so far), for finding angle "Z", would I just take the scale factor and do something with it towards the 85 degree? The scale factor is 5/3.

#17
Quote by TheEndHasNoEnd
because the triangles are congruent, i.e. exactly the same shape.

Are you sure?

I wouldn't be.

The triangles are similar, if they have the same size they would be congruent. (I'm using a dumbed down explanation of congruence but it's good enough here.)

And to the pythagoras dude; pythagoras didn't take the cosine rule and drop a term.. Hell he wasn't even a person, pythagoras didn't actually exist (shock horror) It was a school of mathematics, but as mathematicians were looked down upon (much like today tbh) the scholars didn't want to be associated with the mathematics so published everything under the name Pythagoras.. Which is said to be the name of a local sheppard.

To add further insult to injury, the pythagoreans didn't even invent pythagoras's theorem. It was known long before that, I believe the ancient babylonians are the earliest known nation to use the pythagoras relation.


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#19
Quote by TheEndHasNoEnd
Hmm, maybe I need to check up on my definition of congruent

But I'm pretty damn sure it's 85.

Yeah, it is 85.. But the congruent bit was wrong..

What can I say? I'm a picky mathematician.




EDIT: For clarity:

Similar = same shape
Congruent = same size AND same shape

(for most school stuff those descriptions should suffice.)
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