The completed construction of a regular hexagon is shown below. Explain why ACF is a 30º-60º-90º triangle.
1 answer:
<span>ACF is a 30º-60º-90º triangle because of the following:
</span>1) Based on a theorem, in a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : √3<span>
1 </span>→ short leg
2 → hypotenuse
√3 → long leg
<span>
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.
</span><span>Using Pythagorean theorem.
</span>a² + b² = c²
1² + b² = 2²
b² = 2² - 1²
b² = 4 - 1
b² = 3
√b² = √3
b = √3
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</span>1) Based on a theorem, in a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : √3<span>
1 </span>→ short leg
2 → hypotenuse
√3 → long leg
<span>
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.
</span><span>Using Pythagorean theorem.
</span>a² + b² = c²
1² + b² = 2²
b² = 2² - 1²
b² = 4 - 1
b² = 3
√b² = √3
b = √3
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</span>
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