Question
The radius of a regular octagon is 10 centimeters. Identify the calculation that should be used to find the apothem.(1 point) Responses a=10cos(22.5°) a equals Start Fraction 10 over cosine 22.5 left parenthesis 22.5 degrees right parenthesis End Fraction a=10cos(22.5°) a equals 10 cosine left parenthesis 22.5 degrees right parenthesis a=10sin(22.5°) a equals Start Fraction 10 over sine 22.5 left parenthesis 22.5 degrees right parenthesis End Fraction a=10sin(22.5°)
Answers
GPT-4o mini
To find the apothem (a) of a regular octagon given the radius (R), you can use the formula:
\[
a = R \cdot \cos\left(\frac{\theta}{2}\right)
\]
where \(\theta\) is the central angle of the octagon, which in this case is \(360°/8 = 45°\). Thus, you take \(\frac{\theta}{2} = 22.5°\).
Given a radius of 10 centimeters, the correct calculation to find the apothem would be:
\[
a = 10 \cdot \cos(22.5°)
\]
So the correct response is:
**a = 10 cos(22.5°)**.
\[
a = R \cdot \cos\left(\frac{\theta}{2}\right)
\]
where \(\theta\) is the central angle of the octagon, which in this case is \(360°/8 = 45°\). Thus, you take \(\frac{\theta}{2} = 22.5°\).
Given a radius of 10 centimeters, the correct calculation to find the apothem would be:
\[
a = 10 \cdot \cos(22.5°)
\]
So the correct response is:
**a = 10 cos(22.5°)**.