Question

B) The completed construction of a regular hexagon is shown below. Explain why AACF is a 30°-

60°-90° triangle. (10 points)

Answer 1

ACF is a 30º-60º-90º triangle because of the following:

1) Based on a theorem, in a 30°-60°-90° triangle the sides are in the ratio 1 : 2 :
`√(3)`

1 → short leg

2 → hypotenuse

`√(3)` → long leg

Side length of the hexagon is the short leg of the triangle. It is 1.

r1 is the radius of the incircle in a regular hexagon. 2(r1) is the diameter of the incircle. It is also the hypotenuse of the right triangle. It is 2.

Using Pythagorean theorem.

`a^2 + b^2 = c^2`

`1^2 + b^2 = 2^2`

`b^2 = 2^2 - 1^2`

`b^2 = 4 - 1`

`b^2 = 3`

`√(b^2) = √(3)`

`b = √(3)`