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You can’t solve this brainlets

Anonymous Thu 04 Nov 23:34:28 2021 No.13820152 View Reply Original Report

Quoted By: >>13820263 >>13820338

If you can’t solve this, you’re a brainlet(I’m one)

Anonymous

Anonymous Fri 05 Nov 2021 00:19:29 No.13820263 Report

Quoted By: >>13820271 >>13820279

>>13820152
I hate geometry.
Let $a = BC, b = AC, c = AB, h_a = AQ, h_b = BR, h_c = CP$ . Of course we know the last three.

$sinA =\frac{h_b}{c} = \frac{h_c}{b} \implies b h_b = c h_c$

In general
$ah_a = bh_b = ch_c \text{ (1) }$
Law of cosines:
$b^2 = a ^2 + c^2 - 2ac\cdot cosB \iff cosB = \frac{a^2+c^2-b^2}{2ac} \implies sin^2A = 1 - \left(\frac{a^2+c^2-b^2}{2ac}\right)^2$
Because of (1): $a^2+c^2-b^2 = k\cdot a^2$ for some $k$ (we can compute it). So
$sin^2B = 1 - \frac{k^2a^2}{4c^2}\iff \frac{h_a^2}{c^2} = 1 -\frac{k^2}{4} \left(\frac{a}{c}\right)^2 <br />= 1 -\frac{k^2}{4} \left(\frac{h_c}{h_a}\right)^2$
(Last step because of (1) )
So finally
$c = \frac{h_a}{\sqrt{1-\frac{k^2}{4} \frac{h_c^2}{h_a^2} }}$
And because of (1) we can also compute $a,b$ .
Finally the angle: $B = sin^{-1}\left(\frac{h_a}{c}\right)$ .

I don't care if there is an easier solution. I hate geometry. I don't like geometry problems. I don't understand why I keep trying to solve them.

Anonymous

Anonymous Fri 05 Nov 2021 00:22:32 No.13820271 Report

Quoted By: >>13820305

>>13820263
>why I keep trying to solve them
Because you're a zoomer faggot.

Anonymous

Anonymous Fri 05 Nov 2021 00:24:04 No.13820279 Report

Quoted By: >>13820305

>>13820263
The law of cosines is actually a theorem. Why do people call it a law? Math is not physics

Anonymous

Anonymous Fri 05 Nov 2021 00:35:24 No.13820305 Report

Quoted By: >>13820338

>>13820279
>Why do people call it a law
Don't know, don't care. But I agree with you, "The Theorem of Cosines" or "The Cosine theorem" would be a better name.

>>13820271
>Because you're a zoomer faggot.
That's true but I don't understand how that correlates with solving geometry problems.
Care elaborating?
For the record I rarely look at elementary geometry problems and I just wondered why I don't just ignore them completely.

Anonymous

Anonymous Fri 05 Nov 2021 00:47:04 No.13820338 Report

Quoted By: >>13820597

>>13820305
>I just wondered why I don't just ignore them completely
Because you like it. Nothing wrong with that.

>>13820152
Maybe you can solve it by using Ceva's Theorem or Menelaus'

Anonymous

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Anonymous Fri 05 Nov 2021 02:25:31 No.13820597 Report

Quoted By:

>>13820338
Tried that didn’t get really far

Anonymous

Anonymous Fri 05 Nov 2021 03:12:51 No.13820730 Report

Quoted By:

I'm religiously opposed to solving puzzles with silly triangle diagrams. Do it without the diagrams, category theorist!

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