Question

The completed construction of regular hexagon is shown below explain why act is a 30-60-90 triangle

Answer 1

In a 30°-60°-90° triangle,  the length of the longer leg is √3 times the length of the shorter leg and  length of the hypotenuse is twice the length of the shorter leg.

How to explain the reason

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

Based on a theorem, in a 30°-60°-90° triangle, it is said that the length of the longer leg is √3 times the length of the shorter leg and  length of the hypotenuse is twice the length of the shorter leg,

1 → short leg = 1

2 → hypotenuse = 2

√3 → long leg = √3

Using the Pythagorean theorem., we have that

a² + b² = c²

1² + b² = 2²

b² = 2² - 1²

b² = 4 - 1

b² = 3

√b² = √3

b = √3

Thus, in a 30°-60°-90° triangle,  the length of the longer leg is √3 times the length of the shorter leg and  length of the hypotenuse is twice the length of the shorter leg.

Learn more about Pythagorean theorem here:

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