Calculate the height h | Important Geometry and Algebra skills explained

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Calculate the height h | Important Geometry and Algebra skills explained

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[PunPun-luby]

Thanks Sir. Since I watch your video I just visits your channel everyday.

[arthurschwieger]

Once I had the 35 leg using 21^2 + 28^2 = C^2, I calculated the area of the triangle using (21*28)/2 = 294 and then used another area approach using (35 * h)/2 = 294. This gave me 16.8 for h. There are always different ways to solve math problems. 🙂

[innocentonly]

We get the area of triangle ABC by multiplying 28 by 21 and divided by 2
The same area will be base AB multiply by height h devided by 2 so we get " h " here.

We got AB 35 thanks pytho.., now 1/2(28x21) = 294, 1/2(35xh)= 294, h = (294x2)/35= 16.8

[Copernicusfreud]

I figured out the base length of the largest triangle (35) using the pythagorean theorem, and then I used Heron's formula to calculate the total area of 294 square units. Area = (1/2) * b * h. b =35 and Area =294. h=16.8 units.

[jaldobariya]

We can also sole this by using formula of area
Firstly find the hypotenuse
Its 35
Here angle C is 90°
Therefore we can take
Area of triangle = 1/2 x b x h
= 1/2 x 21 x 28
=
Now taking base 35 and height h
Area = 1/2 x b x h
294 = 1/2 x 35 x h. (from eq-i)
294 x 2/35 = h
h = 16.8
I found this method more simpler than the o e you used in the video.

[uchihataha]

we have AB=35
and cos(CBD)= 0.8
cos(CBD)=BD/BC
BD=0.8×28
h^2=BC^2-BD^2
h=16.8
I use cos and pythagore

[santiagoarosam]

El triángulo es tipo 3, 4, 5 → Hipotenusa =7x5=35 → Area rectángulo =Base x Altura → 28x21 = 35h → h =28x21/35 =16.8
Un saludo cordial.

[MrPaulc]

Nicely done, yet again. A slightly simpler way to obtain leangth AB: AC is 3*7. BC is 4*7. Therefore, AB is 5*7 due to 3-4-5.

[MdArbaz]

I solved this by using trigonometry

Sin beta = Sin beta
Or, 21/28 = h/(28^2-h^2)^1/2
Or, 3/4 = h/(28^2-h^2)^1/2
Or, 4h/3 = (28^2-h^2)^1/2
Or, (16h^2)/9= 28^2-h^2
Or, h^2(16/9+1) = 28^2
Or, h^2(25/9) = 28^2
Or, h = (28^2*9/25)^1/2
Or, h= 28*3/5 = 16.8

[funishawsomish]

using the Pythagorean Theorem 21^2+28^2=35^2 then using that knowledge 1/2(21)(28)=1/2(35(h) then simplified distributed and got 35/2(h)=294 multiplied both sides by 2/35 and got h=84/5

[Duke_Of_Havoc]

[Sin(alpha)] ^2 + [cos(alpha)]^2 = 1


Calculate sin(alpha) and cos(beta) in the two smaller triangles respectively. You won't even need pen and paper for that.

[nigelgordon]

The use of Pythagoras's theorem at the start complicated the calculation. 21/7=3 and 28/7 =4 os you have a right angle triangle with sides in the ratio 3 and 4 so the hypotenuse has to be in the ratio of 5, 5*7 is 35. A lot easier than using squares and square roots.

[renesperb]

If you realize that the two sides are 3*7 and 4*7 it is clear that the hypotenuse has length 5*7 . Hence h = 21*28/35 = 16.8.

[williamwingo]

A slightly different approach:
The whole triangle is 3-4-5 multiplied by 7; so the base AB is 5x7 = 35. Let x be the length of AD; then DB = 35 -- x. Invoking Pythagoras,
h^2 = 21^2 -- x^2 = 28^2 -- (35 -- x)^2; so
441 -- x^2 = 784 -- (1225 -- 70x + x^2) = 784 -- 1225 + 70x -- x^2; adding x^2 to each side, collecting terms, and simplifying:
441 = 784 -- 1225 + 70x; rearranging:
70x = 441 -- 784 + 1225 = 882; and finally:
x = 882/70 = 441/35 = 12.6. (calculation done by hand--honest!)
Now looking at the left-hand triangle and calling up Pythagoras again,
h = sqrt(21^2 -- x^2) = sqrt(21^2 -- 12.6^2) = sqrt(441 -- 158.76) = sqrt(282.24) = 16.8.
Calculator used only for the final step, to take the square root.
Cheers. 🤠

[RoderickEtheria]

84/5=16.8. Triangle was clearly 3-4-5 version of triangle.

[Soumik]

It can be easily done by equating the
Area = Area
1/2 a.b = 1/2 c. h
(21 x 28) = 35. h
h = (21 x 28)/ 35
h = 16.8

[calspace]

I did basically the same thing you did, except that I found AB by noting that this was a 3-4-5 triangle with sides equal to 7x the standard.

[xof-woodworkinghobbyist]

Once I had 35 for AB, I went with the area for the big triangle: 1/2 (AB x h) = 1/2 (CB x AC). Fortunately, I got the same result.
I love your videos, make my old brain work.
Thank you.

[NikAlexS]

🔥 Известная формула
h = ab/c

Взято из формул площади треугольника
S = 1/2 ab
S = 1/2 hc
ab = hc
h = ab/c

Просто запомните площадь прямоугольного тругоника равна половине произведения катетов.
И так же, площадь прямоугольного треугольника равна половине произведения гипотенузы на высоту. 😎

[FaridMITA]

Il. Suffit de considérer l'aire du triangle AB5 de deux manières différentes et on obtient rapidement hc=ab.