Question
The radius of a regular octagon is 10 centimeters. Identify the calculation that should be used to find the apothem.
a=10/sin(22.5)
a=10cos(22.5)
a=10/cos(22.5
a=10sin(22.5)
a=10/sin(22.5)
a=10cos(22.5)
a=10/cos(22.5
a=10sin(22.5)
Answers
GPT-4o mini
To find the apothem of a regular octagon, you can use the formula relating the radius \( r \) and the apothem \( a \):
\[
a = r \cdot \cos\left(\frac{\pi}{n}\right)
\]
For a regular octagon, \( n = 8 \), so:
\[
a = r \cdot \cos\left(\frac{\pi}{8}\right)
\]
The angle \( \frac{\pi}{8} \) in degrees is equal to \( 22.5^\circ \).
Given that the radius \( r = 10 \) cm, the appropriate calculation to find the apothem is:
\[
a = 10 \cdot \cos(22.5^\circ)
\]
Thus, the correct choice from your options is:
**a = 10 \cdot cos(22.5)**
\[
a = r \cdot \cos\left(\frac{\pi}{n}\right)
\]
For a regular octagon, \( n = 8 \), so:
\[
a = r \cdot \cos\left(\frac{\pi}{8}\right)
\]
The angle \( \frac{\pi}{8} \) in degrees is equal to \( 22.5^\circ \).
Given that the radius \( r = 10 \) cm, the appropriate calculation to find the apothem is:
\[
a = 10 \cdot \cos(22.5^\circ)
\]
Thus, the correct choice from your options is:
**a = 10 \cdot cos(22.5)**