Shai Gar's Math Challenge 3

Well, I did some thinkin' for a couple minutes, then realized that I'm on summer vacation and really don't feel like it. But, if I'm not incorrect (which it is pretty likely I am), E is 60 degrees, D = C, and G and F could be found using some equations based on the ASA theorem once the rest is found.

 

Specific answers, rounded to 1 decimal place:

Spoiler

A = Center of Regular Equilateral Pentagram
B = 10cm
C approx 12.4 cm
D approx 14.8 cm
E = 72 degrees
F approx 22.8 cm
G approx 23.9 cm

General Results (trig functions in degrees):

Spoiler

C = B / (cos(36.5))
D = 2B * tan(36.5)
E = 72 degrees
F = B * tan(36.5) * tan(72)
G = B * tan(36.5) / cos(72)

I is nerd!

 

I just realized I don't remember geometry. Oh well, too bad.

 

Whoops! That should be 36, my bad!

360 degrees in a circle (around point A). If you draw segment B from A to each edge, and segment C from A to each vertex, you'll get 10 identical right triangles surrounding point A. So that angle is 360 / 10 = 36. I don't know how, but I screwed up an initial calculation and got 73 degrees somewhere, which led to 36.5... My bad.

 

The answer is three. That is all.

 

My geometry teacher taught me S***

 

Don't worry you forget it all anyway.

 

I absolutely LOVED geometry at the college level! You know - right after calculus. hehe

 

I was good at geometry, but I haven't the memory for math. And it's not abstract enough for the likes of me haha

 

ABSOLUTELY YES. ^^THIS.

I haaaaaate math. Never did geometry in high school, never did trig, just barely got by on college algebra and basic calc.

NO MORE WIRE MATH HANGERS!!!

 

Here you go. Math with Abstract right in its title

http://en.wikipedia.org/wiki/Abstract_algebra

 

My thought process:

I start with Introverted Intuition.

First I take a look at the diagram, and deduce the following in a very short amount of time. (which might be a bad idea considering the diagram does not visually represent to scale what it is implying, but for guesstimations seem close enough).

G > F > C > D > B

G has to be greater than F because it would angle out past it if rotated.

C seems greater than D which looks greater than B, assuming this diagram isn't as far enough off to cause a misread.

G doesn't look to be more than triple B, and might not even be double B.

Therefore, all the measurement variables are between 10 and 30.

Extroverted Feeling then assesses the need for a more specific answer.

If I simply needed to rule out a possible answer above 30 or below 10, then my work is done.

Otherwise, I would proof my work with my Ti and more accurate Se assuming a specific answer was important. However, the problem appears to have already been solved, so my Fe sees no reason to expend the effort.

That's how my mind works. Ni to Fe then Ti and Se.