Great proof! Thanks for sharing.

@PreMath

3 жыл бұрын

Thanks James for the feedback. You are awesome 👍 Take care dear and stay blessed😃

Never heard of Stewart's theorem before. Very interesting! Thanks for the work you put in to your videos.

@PreMath

3 жыл бұрын

Thanks my friend for such an elegant feedback. Thank you so much for taking the time to leave this comment. You are awesome 👍 Take care dear and stay blessed😃

@amirmoshirzade1986

3 жыл бұрын

pythagorean theorem is the result of this theorem,when the triangle is isoscale.

@moneergabriel4139

7 ай бұрын

I know , I have never heard about that theory!!!! I don’t know where it came from?

Very well explained step by step. Presentation faultless. A pleasure to read.

@PreMath

3 жыл бұрын

Thanks John dear for the visit! I put my heart and soul in this video. You are awesome 👍 Take care dear and stay blessed😃 Kind regards Love and prayers from Arizona, USA!

I'm aspirants of CGL from India...when Gagan sir talk about this theorem...we came here and saw proof.. thanks a lot sir..for your hard work

Well I had never even heard of Stewart's theorem until tonight and it's nice to see such an easy and elegant proof. It seems like a useful theorem.

@shobhasingh8960

4 ай бұрын

U can use sin formula in this question to find the answer even faster

Thank you sir, well explained👌🙏

Thank you very much, very helpful

you are still the best explainer one ever! love it.

@PreMath

3 жыл бұрын

Thanks dear friend for the feedback. You are awesome 👍 Take care dear and stay blessed😃 Always good to see you dear

Thank you for a thorough and well explained proof of a formula that I never knew about. As for the the example, rearranging the formula is often not an easy task for students. I would encourage them to substitute the values first. After that there is only one unknown and the process of solving the equation becomes easier and more accessible. For the more able mathematicians in your audience, it’s also worth doing what you did. Thank you.

@PreMath

3 жыл бұрын

Thanks Hassan dear for the feedback. You are awesome 👍 Take care dear and stay blessed😃 Love and prayers from the USA! 😃

my favorite theorem.always liked it. god power you.thanks. whit respect.from Iran💐🙏

@PreMath

3 жыл бұрын

Thanks Amir dear for the visit! I put my heart and soul in this video. You are awesome 👍 Take care dear and stay blessed😃 Kind regards Love and prayers from Arizona, USA!

@amirmoshirzade1986

3 жыл бұрын

@@PreMath you're so kind & professional.A real teacher. In persian culture the teacher & the father are the most respectful persons. Goodluck🙏💐

Great video. You really make math easier and simple for us. Thanks for the video♥️♥️♥️♥️

@PreMath

3 жыл бұрын

You are so welcome dear! Thank you so much for taking the time to leave this comment. You are awesome 👍 Take care dear and stay blessed😃

Didn't know about Mr. Stewart. Taught high school math years ago.

Very elegant and clear.

@PreMath

3 жыл бұрын

Thanks my dear friend for the visit! I put my heart and soul in this video. You are awesome Ken 👍 Take care dear and stay blessed😃 Kind regards Love and prayers from Arizona, USA!

Thank you

Draw a perpendicular line from point A to BC, and let the intersection point be E. Since triangles ABE and ACE are both right triangles and BC=21, we know that BE=5, EC=16, AE=12. We also know that DE=9, so using the triangle theorem for triangle AED, we can derive ED=15.

@catherinekloos8531

3 жыл бұрын

DE = 9 ?,,

@ebi2ch

3 жыл бұрын

@@catherinekloos8531 14-5=9

@PreMath

3 жыл бұрын

Thanks dear for sharing this. You are awesome 👍 Take care dear and stay blessed😃 Kind regards Love and prayers from Arizona, USA!

Very well! You are my idol!

Many many many many thanks for giving it. I have known it just now.

@PreMath

3 жыл бұрын

Thanks Rahman dear for the visit! I put my heart and soul in this video. You are awesome 👍 Take care dear and stay blessed😃 Kind regards Love and prayers from Arizona, USA!

Choose X on BC with AX⊥BC & let AX = h. Area ABC = √{s(s-a)(s-b)(s-c)} = √{27 x 14 x 7 x 6} = √15876 = 126 = ½hx21 → h = 12 → BX = 5 → DX = 9 → AD = √(12² + 9²) = √125 = 15. No need for Stewart’s theorem (to be frank, premath, not only have I never heard of Stewart’s theorem, as so many here haven’t, but the result doesn’t seem to be general enough to deserve a special name).

Sir I am writing competition exams in India very useful sir thanks sir❤️

Wow, that's another pearl of wisdom, there seems to be a real sack full of geometric laws and theorems, and that's only the 2D stuff, makes you appreciate how amazing our world is, and how genius our creator giving us such an organism as the brain, si that we could try to understand it, we never will, of course, I'm convinced we were designed with some great plan in mind. Thanks for sharing, sometimes I can't believe how much better my mind works since following your lessons

thanks a lot

I used a,b,c and Law of Cosines to calculate cos C, then used LofC again with b,n and cos C, all of which are now known, to get d.

@chessdev5320

3 жыл бұрын

basically that's how u prove Stewart theorem using trigonometry.

@PreMath

3 жыл бұрын

Thanks dear for the feedback. You are awesome 👍 Take care dear and stay blessed😃

Nice one Prof.! But i have this question in mind: Is this Stewart Theorem also applicable to a right triangle?

I first heard this theorem very nice theorem sir

@PreMath

3 жыл бұрын

We are all lifelong learners. Thanks Sarma dear for the visit! You are awesome 👍 Take care dear and stay blessed😃 Kind regards

I’ve come to this problem after two years and another method is drawing a parallel line to AB from D and the using Thales theorem and cosine law easily gives the answer

Nice one - very good explanation

@PreMath

3 жыл бұрын

Thanks Okemos dear for the visit! You are awesome 👍 Take care dear and stay blessed😃 Kind regards Love and prayers from the USA!

very well done, thanks for sharing bro

@PreMath

3 жыл бұрын

Thanks dear friend for the feedback. You are awesome 👍 Take care dear and stay blessed😃 Always good to see you dear

Stewart's Theorem will solve the problem nicely, as shown in the video. Another much easier solution can be found if you recognize a 13-20-21 triangle off the bat as two right triangles 5-12-13 and 16-12-20 (four times 3-4-5) back to back, sharing the side of length 12.

Very informative video and nice explanation Sir.

@PreMath

3 жыл бұрын

Thanks Viyush dear friend for the feedback. You are awesome 👍 Take care dear and stay blessed😃 Love and prayers from the USA! 😃

@viyushsingh3435

3 жыл бұрын

@@PreMath thanks sir

Learnt something new from you.... ❤️❤️❤️

@PreMath

3 жыл бұрын

Thanks Hasan dear for the visit! You are awesome 👍 Take care dear and stay blessed😃 Kind regards Love and prayers from the USA!

@waraulhasan2477

3 жыл бұрын

@@PreMath ❤️❤️

Very useful sir.

@PreMath

3 жыл бұрын

Glad to hear that Thank you so much for taking the time to leave this comment. You are awesome 👍 Take care dear and stay blessed😃

Thankfully we have mathematicians in the world. They are weird. Because of that they come up with the most esoteric relationships. Love it. My daughter is a math major at university. I rest my case. ☺

@PreMath

3 жыл бұрын

J Hill you are the best Thanks dear for the visit! You are awesome 👍 Take care dear and stay blessed😃 Kind regards

Absolutely unknown theorem. Never told about at school. Interesting anyway. Thanks.

I have never heard about this theorem, the problem is easily solved by using Pythagoras theorem if we drop the hight from the angle A and consider two triangles with the common side (the hight).

🙏🙏🙏.. amazing 👍

Amazing

I solved this problem using law of cosines twice Fist time I used law of cosines for cosine of angle , second time for length of d

What is the difference between Stewart's Theorem and Apollonius's Theorem?

Can u find the answer by using coordinate geometry or by using some other methods Teach us derivation of ladder theorem

We can find area of ABC (Heron) then we have area of ADC since it is 7:14 ... then we can find angle C that is acute . Then AD ...

@harikatragadda

3 жыл бұрын

Nice 👍

@PreMath

3 жыл бұрын

Thanks dear for the visit! You are awesome 👍 Take care dear and stay blessed😃 Kind regards Love and prayers from Arizona, USA!

@user-mx8sj1nc6v

3 жыл бұрын

@@PreMathThank you. I do agree that this is a good way to present Stewar's formula.

Hi can i ask a doubt why cos(a) = -cos(180-a) can i have a complete proof, anyway nice video i just saw this video on scrolling and it inspired me to check law of cosine and law of sine all by it's proofs. ❤️

Why to memorize such a lengthy formula, if one can do the calculation with the COS-rule at points B or C?

I used Pythagoras' thm'

Ans:15

Nice I haven’t heard it

@PreMath

3 жыл бұрын

Keep watching Rs dear

tks

@PreMath

3 жыл бұрын

Thanks Asus dear for the visit! You are awesome 👍 Take care dear and stay blessed😃 Kind regards

Можно найти cos(B) по теореме косинусов в треугольнике ABC. И по той же теореме из треугольника ABD найти AD.Формула сложная для запоминания.

@saurabhnegi4977

2 жыл бұрын

Прокомментируйте, пожалуйста, на английском, чтобы вас могли понять

@user-sk9oi9jl2g

2 жыл бұрын

@@saurabhnegi4977 One can find cos(B) by the cosine theorem in triangle ABC. And by the same theorem from the triangle ABD to find AD.The formula is difficult to remember.

*Estimated radius of the earth = 6,690 kms using Miles Davis’ Hopetoun Monument photo of the mountains in the background behind the Queensferry bridge and Stewart's theorem* We can use one of Miles Davis' photos, Stewart's theorem & Maple to compute the estimated radius of the earth. kzread.info/dash/bejne/m6GmlMlxacyZgbw.htmlm10s (Look at the frames around 12 mins 10 into seconds the video. These are mountains in Scotland. The video itself presents a qualitative argument that the Earth can't be flat using perspective. I took it further and estimated the radius of the Earth from the photo and using Google Earth and Peakfinder to obtain distances between the observation point, the bridge and the peaks). Stewart's Theorem - en.wikipedia.org/wiki/`Stewart%27s_theorem b^2*m+c^2*n = a(d^2+mn) Stewart's theorem can be used to estimate the radius of the earth from the photo as the earth is large relative to the distances between Hopetoun monument and mountains in the background, and that we can draw a line through Hopetoun monument through Queensferry to each of the mounting which is close to straight. The line through Hopetoun monument through Queensferry to Earl's Seat is almost straight. Also, each of the mountains used in the analysis appear to be "Almost" the same height as the Queensferry Bridge Central Tower. The variables for Stewart's theorem (see webpage, which are the same as it is in this video) are set up as follows: R = radius of the earth (this is what we are estimating) in kms. c = R +0.210, as Hopetoun monument is R + 0.210 kms from the earth's center. d = R +0.210, as the Queensferry Bridge Tower is R + 0.210 kms from the earth's center. b = R + height of the mountain (e.g. 570 kms for Meikle Bin). n = distance from Hopetoun monument to the Queensferry Bridge Tower. m = distance from the Queensferry Bridge Tower to the target mountain (e.g. 45.347 kms for Meilke Bin). a = n + m. *_Analysis 1:_* _Meikle Bin_ height 570 m (appears very slightly above the Tower Bridge on the photo). _Hopetoun Monument - Queensferry Bridge Tower_ distance 38.238 kms. _Queensferry Bridge Tower - Meikle Bin_ distance 45.347 kms. _Hopetoun Monument - Meikle Bin_ distance 83.7 kms (not used in the calculation). fsolve(38.238*(R+.570)^2+45.347*(R+.210)^2 = (45.347+38.238)*(45.347*38.238+(R+.210)^2), R); So, R = 5,263.955827 (kms). *_Analysis 2:_* _Earl's Seat_ height 578 m (appears very slightly above the Tower Bridge on the photo). _Hopetoun Monument - Queensferry Bridge Tower_ distance 38.238 kms. _Queensferry Bridge Tower - Earl's Seat_ distance 55.200 kms. _Hopetoun Monument - Earl's Seat_ distance 93.5 kms (not used in the calculation). fsolve(38.238*(R+.578)^2+55.200*(R+.210)^2 = (55.200+38.238)*(55.200*38.238+(R+.210)^2), R); So, R = 7,007.456001 (kms). *_Analysis 3:_* _Cairnoch Hill_ height 413 m (appears very slightly below the Tower Bridge on the photo). _Hopetoun Monument - Queensferry Bridge Tower_ distance 38.238 kms. _Queensferry Bridge Tower - Cairnoch Hill_ distance 42.557 kms. _Hopetoun Monument - Cairnoch Hill_ distance 80.9 kms (not used in the calculation). fsolve(38.238*(R+.413)^2+42.557*(R+.210)^2 = (42.557+38.238)*(42.557*38.238+(R+.210)^2), R); So, R = 8,468.636324 kms. *_Analysis 4:_* _Ben Lomond_ height 974 m (appears the same height as theTower Bridge on the photo). _Hopetoun Monument - Queensferry Bridge Tower_ distance 38.238 kms. _Queensferry Bridge Tower - Ben Lomond_ distance 78.684 kms. _Hopetoun Monument - Ben Lomond_ distance 116.5 kms (not used in the calculation). fsolve(38.238*(R+.974)^2+78.684*(R+.210)^2 = (78.684+38.238)*(78.684*38.238+(R+.210)^2), R); So, R = 6,020.278843 kms. *Let’s average these estimates* So, R (average) = (1/4)*(5263.955827+7007.456001+8468.636324+6020.278843); = 6,690.081748. So, the estimated radius of the earth (assuming it is a sphere) is *6,690 kms* (the average actual radius is 6,371 kms). Fairly close. It is over estimated by about 5%. Who need Eratosthenes and two sticks in the ground to measure the radius of the Earth when we have a Miles Davis photo and Stewart's theorem 😁.

cool

AD^2=12^2+9^2 =144+81 AD=V225=15

Solved using cosine rule 🤟🤟🤟 , but great proof................ and what about proof of other theorems i.e, ladder theorem

@PreMath

3 жыл бұрын

Thanks Aryan dear for the feedback. You are awesome 👍 Take care dear and stay blessed😃 I'm working on other theorem as well. Stay tuned.

@Aryan_Giri01

3 жыл бұрын

@@PreMath Always 😇😇😇 , but bring some olympiad level problem plzzzz

Area ABC (formula Erone) = √p(p-a)(p-b)(p-c) , ove p è il semiperimetro di ABC e a , b, c sono le misure dei lati rispettivamente opposti a A,B,C Risulta area ABC =S =126, ma la stessa area è uguale anche al prodotto di BC per l’altezza AH=h , diviso 2 cioè S =21*h/2=126 da cui h=126*2/21=12 BH=(teor. Pitagora )= √(c2-h2)=√(169-144)=5 DH=BD-BH=14-5=9 AD=√(DH2+h2)=√(81+144)= √225= 15

Well d=-15 (negative 15) is also a solution. Thank you Sir. 👍

@eladiond

3 жыл бұрын

That,s not real. A length is positive in this case. Else AD is out of the triangle.

@mithutamang3888

3 жыл бұрын

@@eladiond No, that's it's real is also negative area!!! 😁😁👍👍

Co oscendo i 3 lati conosco i 3 angoli del triangolo grande(teorama di carnot)... Quimdi dei triangoli piccoli conosco 2 lati e l'angolo compreso.... Perciò conosco il terzo lato x

Please all theorems in one video. No need proof