Can This Be Solved?

[@martinii7904]

Such complicated solution for a simple problem

[@Budgeman83030]

I’m watching this at 3:30 in the morning, figuring out triangles is fun to watch but way too deep of a subject to try and solve using trigonometry

[@brain_station_videos]

A little rest might make them seem way less daunting :)

[@Budgeman83030]

I mostly watch this type of video when it’s really slow at work. If I’m really feeling lucky, I try to work some math videos out before playing. This video was one of those that I’ll put off when I’m on my days off when I get caught up on my sleep

[@ffgamerjay5456]

Bro as a class 10 student I took just 10-20 seconds to know the answer in my mind Explanation : Here the two triangles are similar by SAS property Given angle is 45 so by linear angle property second angle also 45 A side is common Given in the question that two sides are same So they are similar By CPST : The angle we want is also 15

[@Budgeman83030]

@@brain_station_videos I was at work and I was watching math videos to make my night go faster

[@Budgeman83030]

@@ffgamerjay5456 forty + years ago when I was in tenth grade, geometry was my worst subject. It’s slowly coming together, it’s just taking a little bit of research

[@colettecolettecolettecolette]

This is simple but actually briliant

[@MohmmedOmer-hq2ho]

Your solution is elegant, and I have a nice approach to tackle your challenge: We need to show that the angle adjacent to theta (a) is equal to 15 degrees. (only) tan 15 = tan (45 - 30) = (tan 40 - tan 30)/(1+tan 40 tan 30) = (1-1/sqrt(3))/(1+1/sqrt(3)) = (sqrt(3) - 1)/(sqrt(3) + 1) = (sqrt(3) - 1)^2/2 (by multiplying by the conjugate of the denominator) = (4-2*sqrt(3))/2 = 2 - sqrt(3) -------- (*) the perpendicular side is equal x+y (in the right isosceles triangle) so: tan a = y/(x+y) -------(**) Suppose the perimeter of the outer triangle is 1 unit. Then: x+y = sin 30 and 2x+y = cos 30 Solve both equations for x: x=1/2 - y x= sqrt(3)/4 - y/2 Solve the system: y = 1 - sqrt(3)/2 x = (sqrt(3)-1)/2 and x+y = 1/2 and 2x+3y = 2 - sqrt(3)/2 recall for tan a : tan a = y/(y+x) = (1-sqrt(3)/2)/(1/2) = 2 - sqrt(3) from (*):- a = 15 done!! and this holds for all triangles # I hope this solution works well for you😃.

[@ffgamerjay5456]

@MohmmedOmer-hq2ho but bro it can be done by similarity of triangles in an easy manner

[@MohmmedOmer-hq2ho]

@@ffgamerjay5456 Could you clarify what I might have missed?

[@ffgamerjay5456]

@MohmmedOmer-hq2ho bro the main mistake that you have done is that you have written Tan 15= tan (45-30). Which is a common mistake that most of the students do If you are in class 10 so you know that we are told the values of : 0,30,45,60 and 90 degrees for each trigonometric identity If tan 15 can be written as tan (45-30) and then tan 45 - tan 30 Then tan 45 can be written as tan (90-45) So, tan 45 = tan 90 - tan 45. ( substituting the values ) 1 = not defined - 1 ( tan 45 = 1 ). ( tan 90 = not defined ) You think yourself is the above written statement true?? No it’s not at all true because a number written as not defined can not be used as a number in an equation HOPE You got to know about your mistake 😉😉🤠

[@MohmmedOmer-hq2ho]

​@@ffgamerjay5456 Absolutely, you bring up an excellent point! The formula: tan(a-b) = (tan(a) - tan(b))/1-tan(a)tan(b) holds for all a, b such that a, b does not equal n*pi/2 where n is an odd integer. This is essentially because we cannot have TWO RIGHT ANGLES IN A RIGHT TRIANGLE!! Therefore, for the given case of a right triangle with 45 and 30, this formula works perfectly. I appreciate your solid understanding😉

[@ffgamerjay5456]

@MohmmedOmer-hq2ho 🙏🙏 sorry for my misunderstanding about your concept as I am just a class 10th student and don’t know that much about what you had written so I misunderstood it But still your answer was also correct and definitely your way of solving the question was also correct but I just came with a little bit easier and simpler method to solve the problem 🫶🫶🙏

[@fireff274]

For class 9 angles opposite to equal sides are equalSo that means X=15° 15°=15° by adding both angles Ø=15+15 Ø=30°

[@noobgaming-cf4jd]

x is a side bro..

[@ArijeetMallikAO]

There were guys who introduced Angle Sum Property of triangle and exterior property of triangle.

[@someoneyoudonthavetoworryabt]

Me

[@NehaTyagi-j3e]

Happy to see a class 9 RD question in a KZbin video😆

[@KaivalyaChess]

finally, some cultured person

[@ReenaHgvr]

You will be more happy to know that all the solution is there in KZbin

[@alifmallik1242]

bruh i am in class 10.... i used a didn't calculated using this very hand method... and found the answer

[@AkshatDubey-pm9lq]

Nice and awesome question You are genius ❤

[@AtharwaKumar]

It can be solved even more simply by sine rule

[@hightechgaming757]

awesome bro

[@pratyushkhandelwal7138]

Loved the pun 😂 Awesome explanation

[@prem198102]

You are a genius 😯 you are good in maths.

[@brain_station_videos]

Wow, thanks

[@neelamshukla1144]

SO cool! :)

[@jayabanerjee1876]

Well done

[@donuteater900]

could you make a video on how to solve it using trigonometry?

[@ashutoshshukla8015]

SINE RULE WOULD BE THE BEST SOLUTION FOR THIS.

[@Meow-meow51]

But that only works with a right angle triangle right?

[@ashutoshshukla8015]

@Meow-meow51 no, it is applicable on any general triangle.

[@Meow-meow51]

@@ashutoshshukla8015 oh kk

[@atishayjain5550]

can't we do this using cosine rule?

[@ShankarMahato-ed4zz]

Nice👍

[@gopigupta2501]

Very easy question I am in class 9 I thought that your solution is very big but it's still very easy to do

[@NotTheUltimateBlazefr]

I got the answer without all that huge process... I just used simple rules and theorems and I somehow got the correct answer...

[@shikharsingh4142]

For the first time I used trigonometry for solving this problem and used exactly the same variables as mentioned

[@FingerMoments]

I guessed it in 5 seconds after question appeared I swear

[@RiShabhPandey-1823T]

here is alternate solution use linear pair and sas congruence

[@Philip-qq7ql]

i didnt watch the video but i solved by the thumbnail: t = theta 15 + (180-45) + x = 180 x (far right angle) = 30 t + 15 + 30 + y (far left angle) = 180 t + 45 + y = 180 these equations are equal therefore the two triangles, left and the one which encompasses both the right and left ones have equal angles but are rotated and flipped, if you rotate and flip the left triangle you can see the 45 degree angle matches up with the theta + 15 angle. Therefore theta = 45 - 15, or 30

[@Zomsteve]

So aGooood 😼👍😏

[@papa_mugambo_CK]

Use trigonometry😊😊😊easy solution

[@user-mj8eg1hs1s]

Which software do you use for making this kind of video please

[@rudrajitghosh8955]

I think AOPS

[@VLGgamings]

Easy peasy

[@thecomputer1424]

Damn, very complicated! ☠️

[@SameerSameer-hb1xc]

A 9th grade question done without pen

[@HetParmar-t9g]

Yes is solved

[@PixelProwessTheGameExplorer]

JUST SIMPLY DRAW A LINE “l” PARALLEL TO BC THROUGH A!

[@kartikkumarbhattacharya3876]

It becomes a peice of cake when we use mn cot theorem

[@valluriawesomearts19]

It is 30 degrees

[@GouthamGajula]

Got 30 using trigonometry

[@marioalb9726]

θ = 30°

[@MuhammadFareedRaza]

The answer is 15°

[@Beastshort-69]

Just Got Video Suggestions And Guessed The Angle is 30° by seeing fig 😂

[@brain_station_videos]

👀 Do you know how to prove your guess?

[@Beastshort-69]

@brain_station_videos my brain thoughts are faster than speed of universe expansion 😂

[@rudrajitghosh8955]

Sine rule is sitting behind and laughing ಠ_ಠ( ͡° ͜ʖ ͡°)=ε✄

[@DarshSingh-i9v]

30

[@ragukarthikeyanvelmurugan2363]

Theta 60

[@Noobkings-6]

I got 30

[@shivangssinha1915]

I solved it using trigonometry bro but I find your method more interesting 👍.

[@brain_station_videos]

Thats awesome... actually I also asked at the end to solve the same using Trigonometry and gave some hints...did you use the same approach?

[@raghvendrasingh1289]

👍 tan 45 = h/(y+x) or x = h - y tan 30 = h/(y+2x) or h√3 = y+2(h-y) y = h(2-√3) tan (45+theta) = h/y = 2+√3 45 + theta = 75 theta = 30 degree Other method by m n theorem 2 cot 45 = cot 15 - cot theta 2 = 2+√3 - cot theta cot theta= √3 theta = 30 degree

[@BOARDS2025-u6h]

@@raghvendrasingh1289 bro your both methods are amazing

[@BOARDS2025-u6h]

could you tell how to compute tan 75= 2+root3 without identity for 10th graders

[@raghvendrasingh1289]

@@BOARDS2025-u6h consider a right angled triangle ABC with angle B = 90° , angle C = 75° obviously angle A = 15° take a point D on AB such that angle DCB = 60° if BC = x then DB = x√3 & DC = 2x now angle ACD = 15° hence AD = DC or AD = 2x AB = AD+DB = x(2+√3) tan 75° = AB/BC = 2+√3

[@Anay_718]

0°☠️

[@Vikash_697]

Let's take Hight = h Tan 45 =h / x 1 = h /x X = h Now Tan ø = x /h We known x = h So, Tanø = x/x Tanø = 1 We know Tan 45 = 1, Tan ø= tan 45 Ø = 45

[@bestprojects8333]

How did u take the base as x?

[@bestprojects8333]

I think it should be x+y

[@BOARDS2025-u6h]

I think you applied trigonometry in a non- right triangle or the middle triangle and that's wrong without construction. Sorry the answer is 30 degrees

[@Vikash_697]

@@BOARDS2025-u6h can you explain it

[@BOARDS2025-u6h]

@@Vikash_697 tan 45 = h/(y+x) or x = h - y tan 30 = h/(y+2x) or h√3 = y+2(h-y) y = h(2-√3) tan (45+theta) = h/y = 2+√3 45 + theta = 75 theta = 30 degree

[@VeniMadhavSinghNaruka]

was actually a very easy question. you made it complicated. no construction was needed.

[@brain_station_videos]

Can you share your solution then?

[@tanmaykumarop]

Then share the solution please

[@blessingtshuma3760]

Math Legends 45°-15°=30° ✅

[@BOARDS2025-u6h]

which angles and why you subtracted them?

[@podclipon]

Like ❤(The people who solved before only)

[@atifmiraj07]

Bro we can just use similaraty

[@BOARDS2025-u6h]

in which triangles

[@dolikagupta6851]

You simply solve by using similarity and angle sum property

[@sdivakaran5980]

30/45=3/2 x/135=3/2 x=90 45+90 theta =180 Theta=45

[@sdivakaran5980]

Is itwrong

[@aritrabose8h852]

How are you dividing angles????