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posted

Xuequinox wrote:

(5.2.1.) #67:

"What are the possible side lengths for side ML in the triangle /(at the right)/? Show how you know."

Given information: MS = 10", SL = 4". Angle MSL can be observed to have an obtuse angle.

Edit: All I've been able to assume is that ML could be 12.
I'm going to explain this in detail, forgive me if this is annoying.

a^2 + b^2 = c^2
where a, b, and c are sides of a triangle
(a, b and c are all greater than 0 because they are side lengths)
That's the Pythagorean Theorem, which is the core for solving problems like these.
For example, a triangle with sides of 3, 4, and 5 can be considered a right triangle:
3^2+4^2=5^2
9+16=25
25=25
If we take this one step further, we can find out that:

1. if a^2 + b^2 < c^2, then the triangle is obtuse. generally you have to use the longest side length for c to make this work.
2. if a^2 + b^2 > c^2, then the triangle is acute.

Great, i'm going off-topic.

Let's look at the given first:

  1. MS = 10"
  2. SL = 4"
  3. Angle MSL can be observed to have an obtuse angle

Because MSL has an obtuse angle, (MS)^2+(SL)^2 < (ML)^2.
So let's plug in the values for MS and SL:

10^2 + 4^2 < ML^2
100 + 16 < ML^2
116 < ML^2
(taking the square root of both sides)

sqrt(116) < ML
which approximates to 10.7703296

That's only half of it though.

We need to find a maximum value for ML as well, because think about it:
we can put MS and SL into a single line, can we not? Since a straight line cannot form a triangle anyway, we can take the addition of the two known sides to find the maximum. (sorry, idek if this part will make sense)

So to find our maximum value of ML, we simply add the other two side lengths we know.
ML < MS + SL
ML < 10 + 4
ML < 14

So if we put these two together, our final answer will be:

sqrt(116) < ML < 14


p.s.: i forgot to mention that there's a thing called the Triangle Inequality Theorem.
It's important to know if you want to solve problems like this in the future.

50
posted
aaaaaaaaaaaaaaaaaaaaand you wrote... well, its not exactly an essay.

thanks though, that's actually relatively easy to digest. (seems like I had half of the answer already. I wrote down 'ML < 14"' as my answer, but I didn't know what to do with the minimum.)

51.
posted
That seems like geometry-level stuff isn’t it? Hit me up anytime you need help with that.
Well, I gotta sleep.
26*2.
posted
I'm only one grade advanced in math, so IM2 is something I'm working on for my second semester in 9th grade.

I think it was mostly confusing because no one ever explained this, especially not the teacher. :/

53.
posted
54
you have to put the minimum because they specifically said obtuse angle.
posted

DJ Enetro wrote:

54
you have to put the minimum because they specifically said obtuse angle.
they didn't, I mentioned that "it can be observed", as in it wasn't directly said.

55.
posted
58
posted
why am I awake

57 (husa again that's supposed to be 56 ;w;)
posted
56 then
posted
59
posted
60
posted
61
posted
62
(Crap, sqrt(116) can be simplified to 2sqrt(29))
posted
uwu what are you talking about 63
posted
Look in the previous page
2^6
posted
65
posted
(200 / 3) - 2/3

(edit: shit I forgot the 1/3 wqas supposed to be 2/3)
posted
More like (199/3)-1/3

67
posted
1`2`3
,
1`2`3`2
posted
What is that

69
If it’s some math tell me about it
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