The radius of a regular octagon is 10 centimeters. Identify the calculation that should be used to find the apothem.(1 point)

Question

Responses

a=10sin(22.5°)
a equals Start Fraction 10 over sine 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=10cos(22.5°)
a equals Start Fraction 10 over cosine 22.5 left parenthesis 22.5 degrees right parenthesis End Fraction

a=10sin(22.5°)

Answer 1

To find the apothem \( a \) of a regular octagon with a radius \( r \), you can use the formula:

\[ a = r \cdot \cos\left(\frac{360}{2n}\right) \]

where \( n \) is the number of sides of the polygon. For a regular octagon, \( n = 8 \), so:

\[ a = r \cdot \cos\left(\frac{360}{16}\right) = r \cdot \cos(22.5^\circ) \]

Given that the radius \( r \) is 10 centimeters, the calculation for the apothem would be:

\[ a = 10 \cdot \cos(22.5^\circ) \]

So the correct response would be:

a = 10 cos(22.5°)