@@isavenewspapers8890wouldnt yiubagree a lot kf people are notngoong to.think to duplicate the trisngle likenthat but it doesnt mean they arent good at math or are.not.very.smart and isnt there ankther way to solve without that like breaking up the 54 degree angle into 36 amd 18 or another method maybe? Thanks for sharing.
We can calculate cos36° by x=36°=π/5 5x=π 2x=π-3x sin(2x) =sin(π-3x) sin(2x) =sin(3x) Then we can just use their formulas, to form a quadratic in cosx and find cos36° by using the quadratic formula
I guess we can make hypotenuse of any length we like and will end up with a quadratic equation that will give the side length corresponding to that degree
I don't think so. This is possible since 36 is a factor of 180 which is the angle sum of a triangle. You can construct those isosceles triangles with angles 36°, 72° or 108°, all are multiples of 36°. If that angle is not 36°, say 35°, that's not that easy.
No we cannot do it for every angle The reason why we could do for 36° is cause 36*5 = 180° so it could be broken into many issocles parts tht had 72*2 and a 36
let 'a' be some constant (totally not cosθ) a = x/2 2a = x we are given 36 degrees. Multiply that by pi/180 and we get pi/5 Let pi/5 = b use the mclaurin series of cosθ *coughs* I mean 'a' to find 'a'. a = 1 - b²/2! + (b^4)/4! - (b^6)/6! + (b^8)/8! - (b^10)/10! ..... Compute the value of pi by finding the value of pi/4 and multiplying it by 4 compute the value of pi/4 by integrating from 0 to 1 sqrt(1 - x²) dx after realizing you cannot use trignometric substitution, proceed to use the binomial theorem to break it up into infinite parts and integrate those After finding the value of pi, use the binomial theorem once again to find the exponentials of pi. Thus we arrive at our answer
Let the missing sides be x and y Then * Xy÷2=6 (area formula) ** X²+y²=5² (Pythagoras) From * 2xy=6×4=24 Adding * and ** and substracting * from ** we get x²+y²+2xy=49 ° x²+y²-2xy=1 °° In ° the lhs is the Expansion of (x+y)² So x+y=√49=7 In °° the lhs is the Expansion of (x-y)² So x-y=√1=1 Adding ° and °° we get 2x=8 so x=4 and substituting this in any equation we will get y=3 Thus the sides are 3 and 4
This triangle is ALMOST like the 3-4-5 triangle, but it's 36 degrees instead of 37. If I approximate it to 37 though, I can say from this triangle and 3-4-5 traingle, x/2 = 4/5 (similar traingles AAA Rule) Hence x = 1.6 approximated in my head in seconds 😎
x = 2.cos(36°) = 2.cos((Pi/5) rad) = 2.((1 +sqrt(5))/4) = (1 + sqrt(5))/2. It is good to know that cos(((k.Pi)/5) rad) = ((+/-) sqrt(5) + (+/-).1)/4 for k = 1, 2, 3 or 4. And as the cos decreases on [0, Pi rad] it is easy to find the signs: cos(Pi/5) = (sqrt(5) + 1)/4; cos((2.Pi)/5)) = (sqrt(5) - 1)/4; cos((3.Pi)/5) = (-sqrt(5) + 1)/4; cos((4.Pi)/5) = (-sqrt(5) - 1)/4. A proof can be obtained considering the 5 complex roots of z^5 = 1 whose sum is 0 and then consider the real part.
@ananttiwari1337 every subject of math has it's own purpose to serve that goes for trig and geometry aswell usually you would want to take a simpler route for answering a question
found it interesting how we actually, when we were using the similarity of the triangles, we made our own version of triangles similarity, as we know, trigonometry is just a way of expressing the ratios between the triangle's sides, we did the same, but we created our own triangle with its own values and we found it, becuase after all, i don't think its really possible to go throught the question without using trigonometry, maybe without using its symboles, anyway that was fun to watch and solve + no hate but completing the squares tops the racines sum/product methode
At 2:50, our AI professor shows a right angle triangle and calls it an isoseles. Labeling the, obviously, 90° angle as 72° This entire video is pure non-sense
but DEAR GOD in heaven dont you agree NONONE wpuld ever think to create that third triangle like you did..the duplicate maybe..it's just out of nowhere no matter how smart you are..hope you can respond..thanks for sharing
I couldn't solve it correctly even though I used Pythagoras identity. I somehow got the wrong answer. I will describe my steps to reach my answer. One angle is 36 degrees. And since this is a right triangle, the other angle should be 54 degrees. Now both angles are proportional to the ratio of 54:36 which simplifies to 3:2. So the sides opposite to those angles must also conform to the same ratio. Since X is opposite to the 54 degree angle and hence is the bigger side, let's rename it as 3y where y is a constant. This makes the other side 2y. Now from the pythagoras identity, (3y)² + (2y)² = 2². This simplifies to 13y²=4 leading y to be 2/sqrt(13). Since X is defined as 3y, then it's value would be 6/sqrt(13). Can someone explain to me where I went wrong?
@amazingcalvin I think your mistake is that the ratio of the sides equals the ratio of the sines of the angles, not the ratio of the angles. That's the sine rule, and so it counts as using trig anyway.
@@SuperCreepo1809 wait a second If he can get pin being second I can get pin being first? Woah I'll try it next video But why would I want to be pinned Hmmm Yeah It's just a waste
You can support our work at
www.patreon.com/BrainStation
golden ratio jumpscare
Yeah, I'm surprised it wasn't mentioned.
Yes
Oh no! I just forgot to mention it
@@isavenewspapers8890wouldnt yiubagree a lot kf people are notngoong to.think to duplicate the trisngle likenthat but it doesnt mean they arent good at math or are.not.very.smart and isnt there ankther way to solve without that like breaking up the 54 degree angle into 36 amd 18 or another method maybe? Thanks for sharing.
Same here
Find X? It’s just below the middle of the adjacent side. No trigonometry needed!
🥲
@@BrainStationAdvanced yoo you made the wizard owl sad
😂😂😂
We don't need calculater or this method
We just need a ruler
Also your is name
Ruler? German one?
@@GoatedツSamosa I see what you did there
@@GoatedツSamosa dark
@@chitradevi9919 darker
We can calculate cos36° by
x=36°=π/5
5x=π
2x=π-3x
sin(2x) =sin(π-3x)
sin(2x) =sin(3x)
Then we can just use their formulas, to form a quadratic in cosx and find cos36° by using the quadratic formula
Wow! With this method we can find out sin/cos for every degree (not just 36°) if given the hypotenuse.....
Thank you sir, for sharing this question!
I guess we can make hypotenuse of any length we like and will end up with a quadratic equation that will give the side length corresponding to that degree
I don't think so. This is possible since 36 is a factor of 180 which is the angle sum of a triangle. You can construct those isosceles triangles with angles 36°, 72° or 108°, all are multiples of 36°. If that angle is not 36°, say 35°, that's not that easy.
Only works for 36. If you try for most numbers, say 10, you don’t get an isosceles triangle
No we cannot do it for every angle
The reason why we could do for 36° is cause 36*5 = 180° so it could be broken into many issocles parts tht had 72*2 and a 36
let 'a' be some constant (totally not cosθ)
a = x/2
2a = x
we are given 36 degrees. Multiply that by pi/180 and we get pi/5
Let pi/5 = b
use the mclaurin series of cosθ *coughs* I mean 'a' to find 'a'.
a = 1 - b²/2! + (b^4)/4! - (b^6)/6! + (b^8)/8! - (b^10)/10! .....
Compute the value of pi by finding the value of pi/4 and multiplying it by 4
compute the value of pi/4 by integrating from 0 to 1 sqrt(1 - x²) dx
after realizing you cannot use trignometric substitution, proceed to use the binomial theorem to break it up into infinite parts and integrate those
After finding the value of pi, use the binomial theorem once again to find the exponentials of pi.
Thus we arrive at our answer
Area of a right angle triangle is 6 CM square and the hypotenuse is 5 cm. Find the height and base.
(5±i√23)/2
3cm, 4cm.
remember your pythagorean triples kids
Let the missing sides be x and y
Then
* Xy÷2=6 (area formula)
** X²+y²=5² (Pythagoras)
From * 2xy=6×4=24
Adding * and ** and substracting * from ** we get
x²+y²+2xy=49 °
x²+y²-2xy=1 °°
In ° the lhs is the Expansion of (x+y)²
So x+y=√49=7
In °° the lhs is the Expansion of (x-y)²
So x-y=√1=1
Adding ° and °° we get 2x=8 so x=4 and substituting this in any equation we will get y=3
Thus the sides are 3 and 4
This triangle is ALMOST like the 3-4-5 triangle, but it's 36 degrees instead of 37.
If I approximate it to 37 though, I can say from this triangle and 3-4-5 traingle, x/2 = 4/5 (similar traingles AAA Rule)
Hence x = 1.6 approximated in my head in seconds 😎
marks given =0 for approximation👍
Me learning instead of scrolling shorts 😊 yeaa....
Perfect!
x = 2.cos(36°) = 2.cos((Pi/5) rad) = 2.((1 +sqrt(5))/4) = (1 + sqrt(5))/2.
It is good to know that cos(((k.Pi)/5) rad) = ((+/-) sqrt(5) + (+/-).1)/4 for k = 1, 2, 3 or 4. And as the cos decreases on [0, Pi rad] it is easy to find the signs: cos(Pi/5) = (sqrt(5) + 1)/4; cos((2.Pi)/5)) = (sqrt(5) - 1)/4; cos((3.Pi)/5) = (-sqrt(5) + 1)/4; cos((4.Pi)/5) = (-sqrt(5) - 1)/4.
A proof can be obtained considering the 5 complex roots of z^5 = 1 whose sum is 0 and then consider the real part.
It's fine if you solve it with trigonometry these types of questions are usually meant to be solved with trig
then you don't really learn anything by doing thaf
@ananttiwari1337 every subject of math has it's own purpose to serve that goes for trig and geometry aswell usually you would want to take a simpler route for answering a question
found it interesting how we actually, when we were using the similarity of the triangles, we made our own version of triangles similarity, as we know, trigonometry is just a way of expressing the ratios between the triangle's sides, we did the same, but we created our own triangle with its own values and we found it, becuase after all, i don't think its really possible to go throught the question without using trigonometry, maybe without using its symboles, anyway that was fun to watch and solve + no hate but completing the squares tops the racines sum/product methode
does this work for all circles?
x is adjacent to 36^o
Why is every calculator I’m trying saying cos(36) is -0.12796…? It’s not even supposed to be negative
There are two modes one is radians one is degrees put it in degrees mode (sometimed written deg) and you get the same value he gets in the video
@ Thanks so much 😌
Now i will flex this in school. This is cool.
I think we can find cos36. Using 5x=90. Then using cos(2x + 3x). I tried it. It is not as lengthy as you think 😅
Square root of 2 & gave it in 1 sec after seeing the hypnotuse
nope
Angles would have to be 45-45 for that
At 2:50, our AI professor shows a right angle triangle and calls it an isoseles. Labeling the, obviously, 90° angle as 72°
This entire video is pure non-sense
can't we use cos 90 ?
It’s cosine. Not cause.
So cos 36° = (1 + √5) / 4. Cool!
Trigonometry not allowed 🤨
@@alexandermorozov2248 this isnt a solution. This is clearly an observation.
Me not knowing trigonometry
not needed
@BrainStationAdvanced I forgor to add anyway
Like
Me not knowing trigonometry anyway
Me too
but DEAR GOD in heaven dont you agree NONONE wpuld ever think to create that third triangle like you did..the duplicate maybe..it's just out of nowhere no matter how smart you are..hope you can respond..thanks for sharing
You will
E=MC2=X
Angle side angle done
I couldn't solve it correctly even though I used Pythagoras identity. I somehow got the wrong answer. I will describe my steps to reach my answer.
One angle is 36 degrees. And since this is a right triangle, the other angle should be 54 degrees. Now both angles are proportional to the ratio of 54:36 which simplifies to 3:2. So the sides opposite to those angles must also conform to the same ratio. Since X is opposite to the 54 degree angle and hence is the bigger side, let's rename it as 3y where y is a constant. This makes the other side 2y. Now from the pythagoras identity, (3y)² + (2y)² = 2². This simplifies to 13y²=4 leading y to be 2/sqrt(13). Since X is defined as 3y, then it's value would be 6/sqrt(13).
Can someone explain to me where I went wrong?
@amazingcalvin I think your mistake is that the ratio of the sides equals the ratio of the sines of the angles, not the ratio of the angles. That's the sine rule, and so it counts as using trig anyway.
2cos(36 degrees)=(1+Sqrt[5])/2 starts with 1.618 It’s in my head.
it's the golden ratio!
But you used trig
Rather contrived, and convoluted.
I liked how he used po shen law method
X,2×+5=8
Nice
i was waiting so long for him to say golden ratio
The small triangle does not have 2angles of 62 degrees, that ruined it
72
What you mean? The X is already there bro
X=1.2
Also, the chilling guy or girl who just wrote it like arccos without any solutions and even more get high scores😂
Just measure the third one side and done pythagoras yah baby:)
twitter
Just put the calculator in the bag lil bro
Second!,The video is great!!❤❤🎉🎉😮😮😊😊
Please pin!!😅😉
@@SuperCreepo1809 wait a second
If he can get pin being second
I can get pin being first?
Woah
I'll try it next video
But why would I want to be pinned
Hmmm
Yeah
It's just a waste
@ZDTF Haha!, you could get pinned by getting the first!, if you want😁😁
I hate these AI voices
deal with it lol, or just dont watch at all
@@ClunkyFunk-m8q yeah not going to watch, just my parting words
😓
true.... i do respect soooome people using these voices (like halfbreadchaos) but most ai voice users are lazy..
Lol also used AI to make the video and solved the problem