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I am trying to finish geometry over the summer.

I am trying to finish geometry over the summer.-example-1

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Great. If you like it there's more geometry to learn than you can in one lifetime, so you're never finished.

Anyway, this is the 30/60/90 right triangle, which you'll soon learn is the biggest cliche in trigonometry. It's a pretty basic object, being half an equilateral triangle. So if the hypotenuse is
s the small side is
\frac s 2 and the middle side
h (which would be an altitude of the equilateral triangle). We write the Pythagorean Theorem:


(\frac s 2)^2 + h^2 = s^2


\frac {s^2}{4} + h^2 = s^2


h^2 = \frac 3 4 s^2


h = (√(3))/(2) s

So the sides opposite 30/60/90 respectively are in the ratio of
\frac 1 2 : (√(3))/(2) : 1 or equivalently
1 : √(3) : 2.

We have E=30, F=60, G=90, with respective opposite sides FG:EG:EF in ratio
1 : √(3) : 2. From the ratios we get


(FG)/(1) = (EG)/(√(3)) = (EF)/(2)

A.
EG= (√(3))/(2) EF \quad TRUE

B. FALSE,
EG=√(3) FG

C. FALSE,
EF=2FG

D. TRUE (see above)

E. TRUE (see above)

F. FALSE (see above)

That looks good.


User Faffaffaff
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