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25 Points!!!!

The completed construction of a regular hexagon is shown below. Explain why △ACF is a 30º-60º-90º triangle.


Here is what i have so far, Can anyone help me finish this proof out? thanks!

1) Based on the theorem of a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : √3
1 → short leg
2 → hypotenuse
√3 → long leg
Since this is a regular hexagon that means that each side is the same length. A normal hexagon equivalent and has six angles of 120° .Angle F must then equal 60 degrees because it is half of the angle of the regular hexagon.

25 Points The completed construction of a regular hexagon is shown below Explain why ACF is a 30º60º90º triangle Here is what i have so far Can anyone help me f class=

Respuesta :

baabaagreysheep
You can prove that angle C is 30°. This is because we know that angle B is 120° also, and cointerior angles add to 180°, which makes angle BCF 60°. Then we can divide this by 2 as angle BCF is bisected by AC, so therefore angle ACF is 30° as 60 ÷ 2 = 30.

You can then prove angle A is 90°. First we can find angle BAC because it is part of a triangle, and angles in a triangle add to 180°. This means we can do 30 + 120 = 150, and 180 - 150 = 30° which is angle BAC. Then we do 120 - 30 = 90, as the whole of angle BAF is 120°.

I hope this helps!
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