Fun Geometry: Find h

#brainexercise #matholympics
Fun Geometry: Find h

Comment your answer in the comment section down below

[someonespadre]

Connect the 2 top points, then it becomes clear that the hypotenuse on the left is half of 100 or 50. H is 25sqrt3 after some simple trigonometry.

[ebrahimnedham]

Brilliant in all aspects, solutions and presentation 👌
Keep up the good work👍

[MellencePeanut]

I got the correct answer, 25√3. Great math video! 🙂

[skwest]

I'm going with 25√3
1. We know the sides of a 30-60-90 right triangle are in the ratio of:
1 - ½ - √3/2
With 1 corresponding to the hypotenuse, ½ corresponds to the leg opposite the 30° angle, and √3/2 opposite the 60° angle.
2. If we connect the two vertices at the tops of the left and right sides (the tops of the 'h' legs), we form a new 30-60-90 right triangle whose hypotenuse is 100.
3. Using the relationships cited in #1, we can establish the left and right legs of this new triangle in terms of h, with the left leg being 2√3h/3, and the right leg being 2h.
4. At this point, we can either employ pythagoras and solve the equation:
(2√3h/3)² + (2h)² = 100²
for h, or we can just continue with our knowledge about 30-60-90 right triangles and use the 30°-leg relationship to the hypotenuse to get the equation:
2√3h/3 = 100/2
In either case the result is the same:
h = 25√3
Now to watch the video to see if I got it right.
Cheers!
- s.west

[PrithwirajSen-njqq]

Complete the rectangle. Another rt triangle we will get.
It's two sides other than hypotenuse is
2h (as the side opposite to 30 degree angle of the bigger triangle is h) and 50√3(it is opposite to 30 degree of the new triangle and it's hypotenuse is 100)
Area of the new rt 🔺
=1/2*2h*2h/√3= half of the rectangle =1/2*100*h
Solving
4h/√3=100
h=100√3/4=25√3
Comment plz

[nilsalmgren]

h/√3 + h√3 = 100...h+3h = 100√3....easy solving from there.

[Birol]

My way of solution ▶
for the triangle on the right side:
tan(30°)= h/x
tan(30°)= √3/3
⇒
√3/3 =h/x
√3x= 3h
x= 3h/√3
x= 3√3h/3
x= √3h

for the triangle on the left side:
tan(60°)= h/y
tan(60°)= √3
⇒
√3= h/y
y= h/√3
y= √3h/3

x+y= 100
√3h+ √3h/3 = 100
h(√3+ √3/3)= 100
h(3√3+√3)/3= 100
h(4√3)= 300
√3h= 75
h= 75/√3
h= 75√3/3
h= 25√3 length units

[devondevon]

25 sqrt 3

Draw a line to form a new right triangle (now, the largest of the three).
Hence, the hypotenuse = 100, and Hence, the shortest leg= 50 and the longest
leg = 50 sqrt 3, since it too is a 30-60-90 triangle,
But since it longest leg = the hypotenuse of the triangle to the right, it shortest
leg is 1/2 its hypotenuse hence 50 sqrt 3/2 = 25 sqrt 3 which = h Answer

[ron]

VERY good English compared to some mathematics presenters.

[samueldeandrade]

Funny thing, my mental calculation was Trigonometry. I just thought

(√3+1/√3)h = 100
h = 25√3

in a second.

[PrithwirajSen-njqq]

My previous solution may be shorter
New rt triangle side opposite to 30=50(half of 100)
as well as 2h/√3(as side opposite to 60 is 2h)
Then
2h/√3=50
h=25√3
Pl comment

[taci]

Es gibt eine ganz einfache Lösung mit Pythagoras

[jppcasey]

I came up with 43.3. I don't see "25√3" on my tape measure. I don't understand why videos like this never fully answer the question. If you're given real values, (like degrees and lengths) and you're being asked to solve a question, then you have to solve it completely. Answering a question with a question is not solving it in the real world.

[cyruschang]

h/a = (✓3)/2
h/b = 1/2
a^2 + b^2 = 100^2 => (4h^2)/3 + 4h^2 = 10000 => 4h^2 (4/3) = 10000 => h^2 = 30000/16 => h = 25✓3

[DhurataMyftiu-zruw]

Vetem kaq do te them . Ne nje trekendesh kenddrejte kateti perballe kendit 30 grade eshte sa 1/2 e hipotenuzes. Te tjerat jane veprime matematike.