Calculate the height h | Important Geometry and Algebra skills explained
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Жыл бұрынLearn how to find the height h in a right triangle. Important Geometry and Algebra skills are also explained: Pythagorean Theorem, Congruent Triangles Theorem; Two Tangent Theorem. Step-by-step tutorial by PreMath.com
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Calculate the height h | Important Geometry and Algebra skills explained
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@bigm383 Жыл бұрын
Thanks for another stepwise explanation!❤🥂
@PreMath Жыл бұрын
You are very welcome! Thanks for your continued love and support! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀
@misterenter-iz7rz Жыл бұрын
AD is 25, by pythagorean theorem, so DB is 25 in an isosceles triangle, then CB is 25+7=32, and thus AB is 40, by pythagorean theorem again, now EB is one half of AB, is 40/2=20, therefore h=15, also applying pythagorean theorem. 😃
@PreMath Жыл бұрын
Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@normanc918 Жыл бұрын
I did the same.
@davidshen5916 Жыл бұрын
BD*AC=CE*AB
@harrymatabal8448 Сағат бұрын
Excellent
@BKNeifert Жыл бұрын
This is how math should be taught. Geometry is a lot like poetry, when you're watching someone solve it. If I ever taught an English Class, I'd pull up one of these types of videos, and teach them to apply the same skills in this, to their poems. Nobody thinks like that, though, but that's also why we have a lot of people who can't think. They always want words to have ambiguity, but a good reader will follow the logic of the poem's words on the page, the same way they'd follow this guy's presentation. Like, poetry is exactly like this video. You're being walked step by step to the answer. And each verse breaks the logic down into simpler bits. Good poetry, anyway is like that.
@georgecaplin9075 4 ай бұрын
I solved it, (probably the same way most others did), by connecting A and D, making that the hypotenuse of the triangle ACD, solving for the length AD, (which is also DB), which gives us BC, from which you can solve for AB, half of AB is BE, then you have all the values to “plug in to” the Pythagorean theorem.
@vara1499 Жыл бұрын
Great solution!.
@eminwadiogbu1566 Жыл бұрын
I just love this question. Keep up the good work sir.👍🏾
@leslievincent20 Жыл бұрын
Excellent I got this one.
@arvindhshennaiah5659 Жыл бұрын
Very nice explanation.
@soli9mana-soli4953 Жыл бұрын
Setting AE=EB=x and DB=y, I constructed two equations, the first by applying the Pythagorean theorem to the triangle ABC (24)^2+(7+y)^2=(2x)^2 I found the second equation by applying the proportions to the two similar triangles ABC and EBD 2x:y=(y+7):x hence 2x^2=y^2+7y whose solutions are x=20 and y=25 Finally, to find h it is enough to apply the Pythagorean theorem again to the triangle EBD, the sides EB and DB being known
@muttleycrew Жыл бұрын
ABC is similar to DBE so once you know that ABC is in the proportions of a 3,4,5 triangle (it's 8x3, 8x4, 8x5) you know that DBE must also be in the proportions of a 3,4,5 triangle. You know that the hypotenuse is 5x5 = 25 so that leaves the other sides being 20 and 15. From similarity h must be the shortest side so that's h = 15.
@PreMath Жыл бұрын
Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@TDSONLINEMATHS Жыл бұрын
Great
@sail2byzantium Жыл бұрын
Excellent! Very memorable. I need to do a better job in remembering as you show here that one can actually MANIPULATE figures and shapes to solve them, rather than being just stuck with what is given to try to deductively figure it out. Thank you, PreMath!
@PreMath Жыл бұрын
Excellent! You are very welcome! Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@davidbrown8763 Жыл бұрын
Thanks for a great challenge which gave me much pleasure to solve.
@NoraBhsas Жыл бұрын
Me having an English degree and not having anything to do with Geometry actually listening and enjoying this explanation
@juanpabloalvarado2721 Жыл бұрын
Thanks for the explanation, needs for me to see 100 times until I try by myself but I going to get it, Thanks again
@HappyFamilyOnline Жыл бұрын
Another great video👍 Thanks for sharing😊😊
@PreMath Жыл бұрын
Thank you too You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@AnonimityAssured Жыл бұрын
An in-the-head quickie if one recognizes two familiar Pythagorean triples. Spoiler alert. An auxiliary line segment can be imagined linking points A and D. We can immediately recognize a 7-24-25 triangle in the top left, so AD = 25 units. Triangles ADE and BDE are congruent, so DB must also be 25 units. CB = 7 + 25 = 32 units. 24 is three-quarters of 32, so ABC is a scaled 3-4-5 triangle. Therefore, AED is also a scaled 3-4-5 triangle, so: h = 25 (3 / 5) = 15 units. Edited to correct a small typo.
@PreMath Жыл бұрын
Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@alster724 Жыл бұрын
Super easy. After seeing the Similarity Theorem, the problem became a piece of cake and solved it off the bat before I can finish the video.
@PreMath Жыл бұрын
Great job! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@gideonlapidus8996 Жыл бұрын
I love this one just think out the box
@samriddhadutta2104 Жыл бұрын
Yes!! I have solved this problem mentally.
@PreMath Жыл бұрын
Excellent! Glad to hear that! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@WaiWai-qv4wv Жыл бұрын
Ok Very thanks
@PreMath Жыл бұрын
You are very welcome! Thanks for your continued love and support! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@alexrocha9191 Жыл бұрын
BOM DIA PROFESSOR Agradeço ao SR por ter aprendido geometria DEUS lhe Abenço Grato
@PreMath Жыл бұрын
So nice of you, Alex Thanks for your continued love and support! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀
@KAvi_YA666 Жыл бұрын
Thanks for video.Good luck sir!!!!!!!!!
@PreMath Жыл бұрын
Thank you too You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@latten531 Жыл бұрын
Thanks, it’s intersting. I used AREA to find out h value. Triangle ABD=300, AB=40, 40xhx1/2=300, 20h=300, h=15 Just a comment from Tokyo, Japan.
@spywhale Жыл бұрын
Thanx your first problem I could work out in my head all the practice is paying off. 🎂
@PreMath Жыл бұрын
Perfect! Glad to hear that! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@user-vw2dw6st5r Жыл бұрын
So easy
@murdock5537 Жыл бұрын
Nice and awesome, many thanks, Sir! sin(φ) = 3/5 = h/25 → h = DE = 15
@mauriciosahady Жыл бұрын
AEDC é um quadrilátero inscritível, correto?
@rudychan8792 Жыл бұрын
More than one hour, I figured it out, h = 15! 😓 I was connecting line CE = AE = BE = it's a Radius!* (Fail) Then, I connect AD, voila! Much-much Easier! It is Triple Phytagoras!!! Great Maths 🙂 👍
@PreMath Жыл бұрын
Great job! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@spiderjump Жыл бұрын
Find AD by Pythagorean theorem , AD = 25. Triangles ADE and BDE are congruent. Hence DB =25. BC =32. AB can be found by Pythagorean theorem, AB= 40. EB=40/2=20 DE can be found by Pythagorean theorem,DE= 15
@PreMath Жыл бұрын
Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@davoodzamani4254 Жыл бұрын
Nice job 🥂
@PreMath Жыл бұрын
Glad you think so! Thanks for your feedback! Cheers! You are awesome, Davood. Keep it up 👍 Love and prayers from the USA! 😀
@DB-lg5sq Жыл бұрын
شكرا يمكن استعمال cos c بصيغ مختلفة
@PreMath Жыл бұрын
You are very welcome! Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@Copernicusfreud Жыл бұрын
Yay! I solved it.
@PreMath Жыл бұрын
Excellent! Thanks for sharing! Cheers! You are awesome, Mark. Keep it up 👍 Love and prayers from the USA! 😀
@rick57hart Жыл бұрын
I did the last step without pythagorean theorem: There are 2 ways to calculate the area of the triangle. (24/2*32) = (40/2*h) + (24/2*7) 20*h = 12(32-7) 20*h = 12*25 20*h = 300 h =15
@muttleycrew Жыл бұрын
Yeah, nice. I did it another way, by knowing that if two sides of ABD are 24 and 32 that's 8x3 = 24, 8x4 = 32. It has to be in proportion to a 3,4,5 triangle since it is a right-angled triangle and the two shortest sides are in a 3:4 ratio. That means the hypotenuse of ABC *_must_* be 8x5 = 40. ABC is also similar to DBE so once you know that ABC is in the proportions of a 3,4,5 triangle you know that DBE must also be in the proportions of a 3,4,5 triangle. You know that the hypotenuse is 5x5 = 25 so that leaves the other sides being 4x5 = 20 and 3x5 = 15. From similarity of ABC with DBE, the length h must be the shortest side so that's h = 15. It's using 3,4,5 triangles and similarity arguments to get h=15. You only really need the Pythagorean theorem once, unless you happen to know that a 7,24,25 triangle is also a right-angled triangle in which case you would never need the Pythagorean theorem at all, at least not explicitly.
@micke_mango Жыл бұрын
If I only had recognized the first pythagorean triangle, I would have solved it in 20 seconds. Now it probably took two minutes for my slow brain to calculate the first hypotenuse in my head. Still a bit proud I didn't need pen and paper...
@liliyakaloyanova377 Жыл бұрын
AD=DB, because triangles ADE and EBD are equal. AD^2=24^2+7^2=576+49=625 AD=DB=25 so CB=32. In triangle ABC AB^2= 24^2+32^2= 576+1024=1600 AB=40 , so DB=40/2=20 . In triangle DBE h^2= 25^2- 20^2= 625 - 400 = 225 h=V225=15
@PreMath Жыл бұрын
Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@luisimtz Ай бұрын
I solved this problem with just mental calculations
@bigboicool101 Жыл бұрын
👍👌
@kevi152 Жыл бұрын
Tan BDE = h/20 =24/32 . So h =3/4 x 20 = 15 . Since triangle ABC is similar to triangle BDE !
@RahmanPatwaryArifur Жыл бұрын
how to do in case ED not in the middle of AB?
@jmlfa Жыл бұрын
Easy! (Again)
@PreMath Жыл бұрын
Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@calspace Жыл бұрын
I am terrible in geometry at knowing where to draw additional line. I used pure algebra. Let us call the length of DB = x and the length of EB = y (so AB = 2y). We have two right triangles, ABC and DBE. Because B is present in both of them, they are similar by AAA. The lengths of the sides of these two triangles (SL;LL;H) are 24;7+x;2y and h;y;x. Therefore, comparing the ratio of the long legs and hypotenuses, we get y:7+x=x:2y. When we multiply this, we get 2y^2 = (7+x)*x = x^2 + 7x. By the Pythagorean theorem, 24^2 + (7 + x)^2 = (2y)^2 576 + 49 + 14x + x^2 = 4y^2 If we multiply the first equation by 2 we get 4y^2 = 2x^2 + 14x. Therefore, 625 + 14x + x^2 = 2x^2 + 14x. Substracting x^2 + 14x from both sides, we get 625 = x^2, or x = 25. So now we know that the sides of ABC are 24; 7 + 25 = 32; 2y. Using the Pythagorean formula we get 576 + 1024 = 4y^2 1600 = 4y^2 400 = y^2 20 = y Now we can either use the Pythagorean formula again to get x^2 - y^2 = x^2 25^2 - 20^2 = h^2 625 - 400 = h^2 225 = h^2 15 = h Or we can use the ratios of sides, either 24:h = 7+x:y 24y = (7 + x)h 24 * 20 = 32h 480 = 32h 480/32 = h 15 = h or 24:h = 2y:x 24x = 2y * h 24 * 25 = 2 * 20 * h 600 = 40h 600/40 = h 15 = h
@PreMath Жыл бұрын
No worries. We are all lifelong learners. Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@sreedharankp9878 Жыл бұрын
👍
@manojitmaity7893 Жыл бұрын
Sir I request you to upload some videos on arithmetic.
@PreMath Жыл бұрын
Sure! Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@RaniDevi-ur8gb 10 ай бұрын
❤❤
@santiagoarosam430 Жыл бұрын
AD=DB 》DB^2=24^2+7^2 》DB=25 》CB=25+7=32 》AB^2=24^2+32^2 》AB=40 》h^2=25^2-(40/2)^2 》h=15 Gracias y un saludo.
@PreMath Жыл бұрын
Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@nandisaand5287 Жыл бұрын
I went trig route. Probably made it harder for myself: CosB=(7+Y)/2X=X/Y 2X^2=Y(7+Y) Mr Pythagoras enters the chat: (7+Y)^2+(24)^2=(2X)^2 =4X^2 =2(2X^2) [Now substitute:] ...=2Y(7+Y) Drop the Algebra hammer: Y^2+14Y+49+576=2Y^2+14Y Combine: Y^2-625=0 Y^2=625 Y=25 Solve for X: 2X^2=7(25)+(25)^2 2X^2=625+175=800 X^2=400 X=20 SinB=24/2X=h/Y h=24Y/2X=24(25)/2(20) h=15
@PreMath Жыл бұрын
Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@williamwingo4740 Жыл бұрын
A slightly different approach: integer Pythagorean triangles abound in this one. We could calculate that AD = 25 by adding 7^2 + 24^2 = 625 = 25^2; or we could just remember that 7-24-25 is an integer Pythagorean triangle. This gives us 25 for DB and 25 + 7 = 32 for CB. Hey, maybe we're onto something here.... Similarly, the big triangle ABC is another integer Pythagorean, 24-32-40, so the base AB is 40 and half the base AE (or EB) is 40/2 = 20. And finally, triangle BDE (or ADE) is a 3-4-5 triangle multiplied by 5, so it's 15-20-25; and h = 15. No peeking, no calculators; just my table of integer-sided right triangles. Coraggio. 🤠
@PreMath Жыл бұрын
Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@williamwingo4740 Жыл бұрын
@@PreMath Thanks. I'm in the USA too, and we need all the love and prayers we can get.
@gamingwithgamer3751 Жыл бұрын
You make my calculations fast
@PreMath Жыл бұрын
Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@seasea5938 Жыл бұрын
利用中垂線性質和畢氏組數。
@amitavadasgupta6985 Жыл бұрын
h/20=24/32=3/4=>h=20×3/4=15unit.
@PreMath Жыл бұрын
Excellent! Thanks for sharing! Cheers! You are awesome, Amitava. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀
@amitavadasgupta6985 Жыл бұрын
@@PreMath thanks.
@AmirgabYT2185 Ай бұрын
h=15
@Reddogovereasy Жыл бұрын
Why is the product of a square root always positive or negative? I've heard you say that hundreds of times but I cannot fathom a reason for that being so.
@nandisaand5287 Жыл бұрын
From problem above: Sqrt[625]=+/-25 (+25)^2=(-25)^2=625 Typically its easier to just think in terms of absolute value, thus positive, but technically it IS [Plus or Minus] Hope that helps.
@rangaswamyks8287 Жыл бұрын
15 answer
@giuseppemalaguti435 Жыл бұрын
H=15,basta utilizzare la similitudine dei 2 triangoli rettangoli
@PreMath Жыл бұрын
Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@comdo777 3 ай бұрын
asnwer=10cm isit
@theoyanto Жыл бұрын
Have we seen this before?😉 Still great example though 👍🏻
@PreMath Жыл бұрын
Glad you think so! Thanks for your continued love and support! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@victorfildshtein Жыл бұрын
let's assume that AE=BE=x △DEB and △ACB triangles are similar We make proportions: EB/BC = CE/AB ⇒ x/BC = (BC - 7)/2x ⇒ 2x² = BC² - 7BC (1) According to the Pythagorean theorem BC² = AB² - AC² = 4x² - 24² (2) Substitute (2) into (1) 2x² = 4x² - 24² -7√(4x² - 24²) 7√(4x² - 24²) = 2x² - 24² We get the biquadratic equation 4x⁴ - 2500x² + 360000 = 0 x₁² = 400; x₂² = 225 x₁ = 20; x₂ = 15 1)Consider the first option: x = 20 AC = 40; BC = √(40² - 24²) = 32; EC = 25 h = √(25² - 20²) = 15 2) Consider the second option: x = 15 AC = 30; BC = √(30² - 24²) = 18; EC = 11 EC < EB the hypotenuse is smaller than the leg. This is impossible. Answer: h = 15
@Tom-os1qv Жыл бұрын
Bruh, I solved it the exact way he did
@simpleman283 Жыл бұрын
15 if u no ur 3,4,5 sets. edit: 24/3 = 8 8 x 5 = 40 40/2 = 20 20/4 = 5 5 x 3 = 15
@PreMath Жыл бұрын
Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@alexniklas8777 Жыл бұрын
Suppose the triangle is Egyptian, then: AB= (24/3)×5= 40; BC= (24/3)×4= 32. Triangle ∆BDE~∆ABC: BE= AB/2= 40/2= 20; BD=BC-CD=32-7=25; DE=h=√(BD^2-BE^2)= =√(625-400)=√225=15. Examination. Let's draw the middle line ∆ABC, the line EF. BF=32/2=16; EF=√(BE^2-BF^2)= =√(20^2-16^2)= 12, i.e. EF=AC/2=24/2=12.
@PreMath Жыл бұрын
Excellent! Thanks for sharing! Cheers! You are awesome, Alex. Keep rocking 👍 Love and prayers from the USA! 😀
@alexniklas8777 Жыл бұрын
@@PreMath Thanks sir 😊
@esegueojogo Жыл бұрын
The famous 3-4-5 triangle....TWICE
@samriddhadutta2104 Жыл бұрын
15
@PreMath Жыл бұрын
Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@jim2376 Жыл бұрын
Fun problem. 25^2 - 20^2 = 225. √225 = 15.
@PreMath Жыл бұрын
Glad to hear that! Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀
@holyshit922 Жыл бұрын
Only thing you have to know for this problem is Pythagorean Theorem
@n.662 Жыл бұрын
Only 1 line!)
@bobgoodman1451 Жыл бұрын
Lots of 345 triangles is an easier solution, but not as robust
@PreMath Жыл бұрын
Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@franciswalsh5469 Жыл бұрын
h is 15
@adilabusafa Жыл бұрын
يتعذر الاشتراك ولا يوجد جرس-يتعذر التعليق-لا أعلم .
@-NguyenChiTai-A Жыл бұрын
This solution in VietNam is for grade 6 and you must be solved between 5 to 8 minutes 😅
@subhajitmukhopadhyay4780 Жыл бұрын
If solved mathematically, it's ok; but when solved geometrically, it's completely wrong.
@antoniolorenzo7644 Жыл бұрын
Intéressant Bon.fin
@PreMath Жыл бұрын
Excellent! Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@faritishmukhametov7063 Жыл бұрын
h=15
@PreMath Жыл бұрын
Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@kostgenn1803 Жыл бұрын
15
@Xyz-sd7ub Жыл бұрын
h = 15
@PreMath Жыл бұрын
Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀
@nusretgulmammadov5144 Жыл бұрын
h=15
@PreMath Жыл бұрын
Excellent! Thanks for sharing! Cheers! You are awesome, Nusret. Keep it up 👍 Love and prayers from the USA! 😀 Stay blessed 😀
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