How smart are you, /b/?

wait

>>716482499
30

>>716482499
40, but the X is in the middle.

Fuck you OP

>>716482499
30

File: Screenshot_2016-12-25-13-03-47.png (288KB, 1080x1920px)

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Found it

File: Untitled.jpg (33KB, 305x453px) Image search: [Google]

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i'm stuck

>>716483537
Yeah, I got stuck there too. I think this was OP's plan. How smart are we really, /b/?

>>716482499
30 degrees

>>716483537
Yeah, that's about as far as I got too

>>716482499
Ain't nobody got time for this shit.

>>716483537
Imagine the left and right side going up. They must meet at a 20 degree angle. Then you can work it out back down. 30 degrees

>>716483807
can you? doesn't that still leave you with two many unknowns...?

>>716483807
how are you going to find the two angles in the auxiliary triangle though? (the one you draw)

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found it

File: Untitled.png (61KB, 305x848px) Image search: [Google]

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>>716483807
hmm

didnt do this in 10ish years

File: meme.png (56KB, 287x812px) Image search: [Google]

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>>716483537
You've been baited, now imagine it like this

>>716483958
Check it by making x = 30. It works.

>>716484168
this is not how deductive reasoning works. We all can solve it by guessing.

>>716484168
??? thats not the point though retard, you're not supposed to 'guess' and find out that way, you're supposed to use trigonometry. Please write out your solution

>>716483958
Remember you can draw straight lines and know that they gave 180 dregrees. So if you know even one more angke with then one blank they must all add to 360. It works. Sorry I'm on phone so can't draw it for you but it works. Put it in and check it.

File: hrehehehe.png (63KB, 789x490px) Image search: [Google]

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x=30

>>716484384
i might be wrong :v

>>716484200
>>716484168
I didn't guess you ass hat. I am telling you to check it that way. God you are lame.

>>716484384
>>716484408

>130 - 50 = 80

heres where you went wrong.
What was your reasoning behind this?

TL;DR: this problem is unsolvable

>>716484384
wrong its 40

>>716484472
>find the answer by plugging the answer in
???

Still waiting on your reasoning

>>716484479
This problem is obviously solvable. All the information that's needed to find x is there.

File: Untitled.png (65KB, 789x484px)

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>>716484408
its probably right. how did you get that though? especially the 130-50 on the left side

>>716484305
>>716484118
There still seems to be too many unknows. Can you show your steps?

>>716484534
I'm waiting on your solution :)
>>716484535
It's probably right because it 'seems' right, but there is no PROOF its right, because you don't use a trigonometric way to find the left corner in the x triangle

60 all angles of a triangle when added must =180 just figure it out from that

>>716483537
Just name the other one y and maje two equations. Alltigether they make 360 and x+y make 180. Then jyst solve the equation

>>716484625
Finding the solution is significantly more challenging than spotting that this is a solvable problem.

>>716484535
never mind, so how can we solve this?

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>>716484625
yeah thats what i thought

so final solution:

guessable but not solveable with the information given?

this is a stupid troll post. basic trig tells you this is unsolvable.

File: wrong.jpg (51KB, 482x377px) Image search: [Google]

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>>716484741
You clearly don't know shit about trigonometry.

>>716484679
no solution
>>716484708
>bla bla i have no solution
Come back to me when you have a solution, oh wait, it's literally unsolvable.
>>716484716
You cant

File: Fgts.jpg (25KB, 309x451px) Image search: [Google]

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After hours and hours, i've found it

>>716484735
Sure, you can measure the angle, but if you dont have a protactor triangle its guesswork yeah.
>>716484792
>trump supporter
tells you enough tbh

i'm done with this thread

>>716484824
It's not unsolvable, you're just retarded and arrogant enough to think that if *you* cannot solve it, then it must be unsolvable. Provide proof that the problem is unsolvable, or fuck off.

>>716484535
You have a mistake where one of the triangles has 190 degrees

>>716484904
I'm not a Trump supporter, faggot.

>>716484893
Pd, it's 30

>>716484625
You could probably do it algebraically. I'm too lazy (aka stupid) to do it though.

>>716484913
Where's your solution? the burden of proof is on you my friend :). Must be hard passing that geometry 101 class kek.

>>716482499
Imagine the two lines meeting at a 20 degrees angle.

Most of you could fins the angle on the left = 50 abd the one on the right = 40.

Thus you have :

50 + a + b = 180 (line)
b + 20 + c = 180 (triangle)
c + x + 40 = 180 (line)

Replacing the unknows :
So x = 50

If you morons are unable to solve this with logic, state the base = 1cm and use cos/sin/tan to work your way up.

>>716484904
the angles stated are not to scale in the image, you cant just measure it cause if you do the stated angle will fuck up your answer

>>716485031
The burden on proof is on the morons claiming that this is an unsolvable problem, seeing as this is very obviously solvable with the laws of sines and cosines. There is also a solution that utilizes only elementary methods, though that one is more challenging.

>>716485057
>more unknowns than equations

nice meme bud

I got 43 and some change

File: 20_60_30_50.png (24KB, 338x585px) Image search: [Google]

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we had this post a few days ago. it's 30 deg.
wasn't too easy to find a solution just by construction.
here is how you can get there.
few key things:
- upper 20° and lower 20° form a equal-sided triangle from which you go on
- use some angle bisectors
- use relative angles between to lines but also (as shortcuts) absolute angles between a line and the horizon for example

>>716485078
I meant physically measuring, but that's cheating ofc :)
>>716485147
Nah bro, i have geometry on my side, but by all means, reinvent math and surprise me!

>laws of sines and cosines

Do you even know what you're talking about? sides arent even given.

Still waiting on your solution boyo.

>>716484679
what this guy said >>716485181

4 uknowns, 3 equasions = unsolveable

>>716485279
>sides arent even given.

I hope this is bait. You obviously set the length of one of the sides to anything you want, and then you solve the problem from there. Clearly you know absolutely nothing about basic geometry.

>>716485260
oh that one could work indeed.

i wanted to add a 75° one somewhere, but it seemed quite hard to figure out where to put it so you get an angle you actually need

>>716485181
You can express b with a, c with b, and x via c. So there are only one unknown. You dumb twat.

>>716485381
>you set the length of one of the sides to anything you want
>>716485451
Please stop talking and take an algebra 101 class, you're embarassing yourself

now i know this is cheap bait, respond to me with a solution

>>716485480
>you set the length of one of the sides to anything you want
Yup, that's how you get there. Something confusing about that?

>>716485557
Stop trying to troll me and present me with a solution.

>>716482499
you can't find because you have no side lengths because you can't use any equations with sin and cos you need at least one side length same with law of sines

>>716485687
You do understand that you can set one side length to anything you want?

>>716485687
wait then that just means you give a side length because if they all scale equally angles wont change....guys im on to something ill get back to you faggots later...

>>716485644
You can set 1 side to anything you want because of triangle similarity. I'm to lazy to work it out thou.

>>716485766
You literally cant you retard

>>716485801
Yes you can, you're just too dumb to understand it.

>>716485801
You can with the laws of sines and cosines

>>716485775
First non-retard that's actually onto a solution.

>>716485826
Explain it to me, if you can you disprove the whole field of trig! I'll wait :) With pictures please, my 'lil peanut brain cant understand otherwise ;'(

>>716483963
>implying everything is given in proper scale

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>>716485884
I disprove the whole field of trigonometry by explaining the obvious fact that angles remain the same regardless of the length of one of the sides of the figure? I think all I'm disproving is one retard's 'understanding' of trigonometry.

File: 15171247_1026389810803439_5193797155321587276_n.jpg (56KB, 960x960px) Image search: [Google]

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can we all agree it is 30, it is so fucking easy, here is one for just the advanced math fags here

>>716486138
15

>>716486150
70

>>716486093
Yes, they stay the same, but the point is you need more than one line to solve this problem, you cant just plug in the other line dipshit. Try it if you dont believe me.

>>716486138
16
Everyone misses the double fries in line two

>>716486206
You don't need any more than one line. The lengths of all the other lines (and all the angles) can be derived from the first line whose length you set and the angles you're provided with. I'd tell you to try it, but you're clearly too retarded to even try.

>>716486206
you have 1 line and all the angles, you can figure the other ones out

a/sin a = b/sin b = c/sin c

it's not that hard to understand

>tfw all these retards that think they can solve this problem

Amerilard education, huh?

>>716486316
>>716486324
Alright boys, do it! You have enough givens right? surely there arent too much unknowns in the equations to be able to solve it, no really, plug those formulas in!

Funny how none of you retards still fail to give me a crystal clear solution, no usage of your formulas in this problem; just babble.
Fucking retards.

>>716486206
any two congruent angles on a plane =180 all angles of a triangle =180 the base says 50+60 so the other angle of the base MUST BE 70 opposite 70 MUST be 110 this is 2nd grade stuff asswipes, just keep figuring each triangle to 180 until you have just one angle left

>>716486138
this is another one of those retarded "tricks" huh

fucking glorious

>>716486456
Thats the whole point retard, there's a point when you literally can't find any more angles because you have too many unknowns.

Still no mathematical solution after more than an hour btw lads. Guess i'm right? :D

>>716486437
This has been solved fucktard. Move on. You might as well stay in your mom's basment. You are never going to fit in to the real world.

>>716485687
>>716485775
these were both my btw

update you can't find it law of sines/cosines wont work because you have two unknowns (side lengths) this would be easier if you had a right triangle somewhere but due to different angles/sides you cannot assume all sides are X some maybe X +/- something so you can assume one side is X

>>716486559
/b/ being too retarded to solve this doesn't prove that there is no solution.

>>716486559
not true

>>716486591
Still no mathematical solution for this problem using your formulas? Then please shut up and gobble on my cock.

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>>716482499

Smart enough to not waste my time proving my intellect to strangers on the internet.

>>716486628
>>716486660
see
>>716486664

>>716486632
i've reiterated the reason why multiple times, there are too many unknowns to use geometrical reasoning to become the angles, let alone use trig formulas. This is my claim, and I back it up. Now I want to listen to the retards that think you can actually solve this.

>>716486628

This guy gets it

>>716486664
can't use law of sines/cosines because...>>716486628

>>716486664
Well done, congratz on disproving all the retards who claimed it was impossible to solve this.

>>716486660
Look who's cock gobbling now hahaha

>>716486628
>>716486759
Wrong, you *can* use the laws of sines and cosines.

>>716486759
well, I just did. why don't you check my work instead of just saying things

>>716486770
thanks

>>716486138
>>716486483
simple linalg and RREF or Cramers rule, but Algebra 101 should be enough

In case anyone wants the solution expressed purely in terms of the four original angles, here it is:

x = arcsin(sin(b + c) / sqrt(csc^2(a) * sin^2(b) * sin^2(d) * csc^2(b + c + d) + 2 * csc(a) * sin(b) * sin(d) * cos(b + c) * csc(b + c + d) + 1))

Where a = 20°, b = 60°, c = 50° and d = 30°.

>>716486664
>be on other post
>posted >>716486665
>go back to /b/ thread list
>see you solved this thread right before my post
>and none of us did quads

>>716486819
>>716486887

>just writing fancy shit to make it equal 30

>>716486814
no you can't you need two side lengths

>>716486987
>Just being too dumb to understand basic trigonometry

>>716486999
look at >>716486664
and observe how two side lengths are generated such that the problem may be solved

>>716486714
You mean like you're doing now. Retard

>>716486999
Wrong. See >>716486316

File: Untitled.png (56KB, 1152x648px)

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here I made it easier for you fucking faggots

>>716486138
16

>>716487263
Aren't the two center angles 80?, not 80 and 70?

>>716487450
never mind i'm blind

You don't even need to use sines and cosines
Just express the upper two angles in terms of x and use sum of all angles of a quadrilateral is 360

>>716487263
Two 80's on the left should be an 80, then a 70.

>>716487450
>>716487528

>>716487263 is just fucking with you

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>>716487263
>110°+80°=180°

Kek

>>716487450
yes sorry for the typo

File: Screenshot 2016-12-25 08.26.13.png (66KB, 1366x768px)

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I constructed the quadrilateral and it's 30. GG you can all go home.

>>716487573
that's not enough to solve as there are two unknown angles in your proposed equation. You need law of sines/cosines

>>716487654
yeah that just shows you can have a computer solve the problem for you

File: idiots.jpg (2MB, 2400x3200px) Image search: [Google]

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Here you go

>>716487724
Yeah I also use wolfram alpha to do my tedious integrals and shit. I use the resources given to me. Welcome to the real world fag.

>>716487724
Most of the time we do, if analytical methods are too tedious we relegate elementary algebra to a computer. If you take any high level Maths course you'd see

Funny how all the morons in this thread who claimed that the problem was unsolvable disappeared after >>716486664 posted the solution.

File: IMG_20161225_152826.jpg (391KB, 1920x2560px) Image search: [Google]

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Always comes to this.

>>716487799
thanks for the chicken scratch

>>716486664
is much clearer

>>716487810
This guy gets it.

>>716487801
Taking Linear Algebra next semester, Maple is going to be my bitch (when it doesn't crash)

>>716487839
it is much clearer but some idiots get confused by letters

>>716487869
Dude I'm taking Linear Algebra next semester too lulz

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>>716487801
Mfw you'd fail a first semester calculus on my University that way.

>>716487801
>>716487810
the point is to provide a proof of this relatively elementary problem so as to indicate that you understand the concepts behind the solution

>>716487827
This is the smartest way to do it, do like 50% of the annoying angles without anything crazy and get a system of eq with 1-3 variables

>>716487082
you can assume only ONE length dumbass

>>716487914
MechE major here you?

Just hoping i get a job and don't end up homeless and use my mediocre math skill to good use

>>716487955
Too bad it doesn't work.

Not enough info. Unsolvable.

>>716482499
60

>>716487916
Absolutely (not him), I got an A in Calc and no calculator (granted all the fractions simplified) but in Diff Eq and Calc 3 they no longer gave a shit if you knew your integrals, or else you don't understand the rest of the problem

>>716487916
Except I already got A's in Calc 1, 2, and 3. My instructor straight up tells you "You just have the computer do it for you" when you're doing shit outside of class.

File: 1482671911407.png (126KB, 1323x952px)

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>>716487955
to bad that doesn't work

>>716487824
That is not a valid solution.

>>716488084
What's invalid about it?

>>716488084
it is

here it is with numbers for the confused people
>>716487799

>>716487999
>>716488068
Well yeah, but once you find out you need one more EQ you just do that

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>>716488064
Kek, murcafags... We need to provide proof behind all the solutions... But i guess that's why your 2 candidates were Clinton and Trump.

>>716487978
again, look at >>716486664
you'd see that one length it assumed to be 1
using that assumed length and two angles, another length is generated using the law of sines. this process is repeated until 2 side lengths of triangle efm are generated, at which point, law of cosines is used to find side length m, which is then used with the law of sines to find the angle x

>>716487994
Maths major with a physics minor. Starting to wish I had studied business and finance

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>>716485910
it's not about the scale but the proportions.

>>716488185
What? You are fucking right. Our gen pop is batshit retarded, don't see me letting it define my own intelligence because i'm surrounded by idiots

>>716488221
Don't we all, I considered math professor at one point but too much BS for me atm

>>716488185
All it said was find x. Now if it said prove x is 30 degrees I would have spent more than 45 seconds on it.

>>716488254
the fuck are you saying nigger
if not to scale, a protractor doesn't work

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>>716488304
>45s
>inb4 can't do it without software

>>716486138
25

>>716486138
15

Here's the solution that utilizes only elementary methods: https://www.youtube.com/watch?v=HQc-54hQ8kw

>>716484384
Your left and right supplement angles excede 180, according to your scribbles

>>716487827
>>716487869

Mfw you retards didn't do it using Vectors. Litaral 5min proof -_-

>>716488597
>>716488637
>>716486187
>>716486150
You guys make me hurt

a= drink
b=burger
c=fries

3a=30
a+2b=20
b+4c=0
b+c+a=?

Solve, you get 5+1+10=16

>>716488896
I feel like i don't have the amount of math you think we should when this is a question straight out of a 16 year olds book

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>>716488979
Yes... Vectors are literaly 8th grade math.

>>716488914
>Too retarded to tell the difference between a multiplication sign and a plus sign.

>>716482499
I have a very rigorous proof of the real value of x, but it is truly too long to post here as it is nearly 30 pages.

However, for the mathematically inclined, I would be happy to provide an outline.

First, you must embed an ellipse with the bottom most line as its short axis that also intersects with the highest point.

From there, it is trivial to define an elliptic curve that defines the ring in which we are working. This will provide a way to convert our cartesian coordinates to get any angle within this geometric shape.

Because of Mordell's theorem, all elliptic curves are cyclic groups and as such all solutions can be generated from a set of points.

Next, we prove that any of these angles cannot be prime. This is trivial and can be left as an exercise. Perhaps I'll give it to my students.

Finally, we can use the modular form of the elliptic curve to solve for any of these angles, as long as they are not prime, which we have just shown cannot be true.

From this, we get that OP is a faggot. QED.

I just loaded up my CAD software and measured it, 30. Easy problem.

>>716488654
that's clever

>>716488654
>>716489308
yeah but i bet it won't work in the general case of the 4 given angles, so you basically have to guess and check and hope youre right

>>716489440
Sure, the solution for the general case is >>716486887. Nothing wrong with recognizing that there is a smarter solution for the four particular angles given here, though.

>>716488914
>Solve, you get 5+1+10=16
that was not the equation you were given to solve try 5+1x10 FAGGOT your stupid makes me hurt

>>716489563
the youtube solution appears elegant but since the method used must be discovered from guessing, it is not actually as elegant as the rigorous proof posted before

>>716488914
>>716489107
>>716489752
ok then what is 5+1x10

inb4 it's not 15

>>716489158
top kek

cant remember laughing so hard in a math related thread on /b/. The part "can be left as an exercise" killed me.

>>716489768
The YouTube method doesn't require "guessing". It just requires one to recognize that drawing a new line at 20 degrees to the base of the triangle creates a series of isosceles triangles that basically solve the whole problem. Recognizing that is of course very hard, which is why that solution is much more clever and elegant than the general one.

>>716482499
fuck your interdimensional shit.

>>716489885
Obviously it's 15, as was posted first by >>716486150.

>>716489885

ok then what is 5+1x10
it's not 15

it is 15

>>716489885
PEMDAS
So go left to right:
5+1=5
5*10=50

>>716490077
its 15

Sorry, I was completely shit with geometry.

>>716490077
hitlarious
>also checked

>>716483537
Two unknowns, one equation. This problem is unsolvable

>>716484516
retard

>>716490658
see
>>716486664

File: picard.jpg (90KB, 1440x1080px)

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>>716484479
>>716484625
>>716484735
>>716484741
>>716484824
>>716484904
>>716485031
>>716485279
>>716485480
>>716485644
>>716485687
>>716485801
>>716485884
>>716486206
>>716486339
>>716486437
>>716486559
>>716486628
>>716486660
>>716486756
>>716486759
>>716486987
>>716486999
>>716487978
>>716488011
>>716488084
>>716490658

>All these fucking retards claiming there is no solution.

>>716482499
sum of interior angles of a 4 sided polygon is always 360.

x is 60

>>716491162
you are an idiot

>>716491203
How so?

>>716491258
b8

>>716491258
there are 2 unknown angles in the quadrilateral and they are not equal. therefore the answer is not necessarily 60 and in this particular case it is definitely not 60

>>716491354
If we assume that they are equal and not trust the image then you're left with a triangle with angles of 60, 50, and 70 which = 180.

While 60 might not be right, it certainly isn't wrong.

>>716486138
25

>>716491479
no, it is quite clearly wrong

>>716491162
>>716491203
>>716491258

Not anyone from this argument. But you have to realize there is no inner 90 degree angle. It would only be 60 if the total was 90, but seeing as the bottom total is 80, meaning the other side has a greater outward angle. Assuming the unlabeled angle on the right of x is still 30, that means x=70

(not sure if I explained this right, but the answer is correct)

>>716491646
If the angles fit the conditions of what a triangle is and fit the conditions of what a 4 sides polygon is then how could it be wrong?

>>716491479
>>716491678
holy shit see
>>716486664
this is the correct answer.
the answer is 30
the picture is how you find it.
there is no other angle that is the correct answer
30 is the only correct answer

>>716491728
because that answer makes other portions of that shape wrong

>>716485910
You can check the other angles then you fucking autist

>>716488164
You'all always need one more. Too many variables and not enough equations.

>>716484479
>>716484625
>>716484824
>>716484904
>>716485031
>>716485279
>>716485480
>>716485644
>>716485801
>>716485884
>>716486206
>>716486437
>>716486559
>>716486660
>>716486756

These posts were mine. Having now looked at the solutions posted, I'll concede that I was retarded.

>>716492539
I will post a shape using the angle you provided to show that does not exist

>>716492539
>100°+50°+50°=360° around a point

File: fucking wrong.jpg (54KB, 844x600px)

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>>716492539
>>716492675

You all retards.
>>716486150
>>716486187
>>716486286
>>716487394
>>716488637

It's 25.

>>716492539
>>716492675
>>716493027
as you can see, if we start with the angles you provided, it disagrees with the original givens in the problem

>>716492556
nice

Using orthonormal axis, trigonometry, scalar product and determinant on vectors, I found this:

There is one and only one solution for this problem
x is such that
tan x = (c*d-b*e) / (b^2+c^2-b*d-c*e)
where
b = tan 60° / (tan 60° + tan 80°)
c = (tan 60° * tan 80°) / (tan 60° + tan 80°)
d = tan 50° / (tan 50° + tan 80°)
e = (tan 50° * tan 80°) / (tan 50° + tan 80°)

>>716493948
does that equal 30? if not, it's wrong see
>>716486664

[ERRATUM on the value of b]
Using orthonormal axis, trigonometry, scalar product and determinant on vectors, I found this:

There is one and only one solution for this problem
x is such that
tan x = (c*d-b*e) / (b^2+c^2-b*d-c*e)
where
b = tan 80° / (tan 60° + tan 80°)
c = (tan 60° * tan 80°) / (tan 60° + tan 80°)
d = tan 50° / (tan 50° + tan 80°)
e = (tan 50° * tan 80°) / (tan 50° + tan 80°)

>>716494054
I've no idea. I'm not very interested in computing my long formula, I'm looking for a way to find a solution that would be expressed with less computations...
Anyway, I'll check my result and give you a numerical approximation.

>>716494054
Approximation given by SageMath is this:
-30.0000000000000
degrees

I guess 30 degrees is the right solution.
I wonder where the minus sign comes from.

>>716493948
This is wrong, it gives the solution x = 180° × n - 30°, where n is any integer.

>>716494179
To be more precise, SageMath gave me this exact result for x (I forced the result to be expressed in degrees in the formula):

180*arctan((tan(4/9*pi)^2*tan(5/18*pi)/((sqrt(3) +
tan(4/9*pi))*(tan(4/9*pi) + tan(5/18*pi))) -
sqrt(3)*tan(4/9*pi)*tan(5/18*pi)/((sqrt(3) + tan(4/9*pi))*(tan(4/9*pi) +
tan(5/18*pi))))/(sqrt(3)*tan(4/9*pi)^2*tan(5/18*pi)/((sqrt(3) +
tan(4/9*pi))*(tan(4/9*pi) + tan(5/18*pi))) - 4*tan(4/9*pi)^2/(sqrt(3) +
tan(4/9*pi))^2 + tan(4/9*pi)*tan(5/18*pi)/((sqrt(3) +
tan(4/9*pi))*(tan(4/9*pi) + tan(5/18*pi)))))/pi

>>716482499
Langley’s Adventitious Angles

https://www.youtube.com/watch?v=HQc-54hQ8kw

>>716495784
Already posted: >>716488654

>>716486664
It seems good.
You don't need to assume that a=1.
You could state that a is unknown, with the only fact about a being that
a>0
and then you get
b = a * sin60/sin70
c = a * sin50/sin70
the other formulas are kept the same,
we notice that:
e is proportinal to a,
f is proportional to a,
therefore m is proportional to a,
therefore e*sin(g)/m is independant from a

the fact that the result is indepedant from a is noticeable, given that it was not clear from the beginning for evybody

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