Question

What does n stand for in the expression?If there are 60 sides, what is the difference between the perimeter and π?

Answer 1

a. The expression represents the perimeter of a polygon:

`n\cdot\sin ((360)/(2n))`

n represents the number of sides of the polygon.

b. If we have 60 sides, then n = 60.

We can calculate the approximation given by the expression as:

`\begin{gathered} n\cdot\sin ((360)/(2n)) \\ 60\cdot\sin ((360)/(2\cdot60)) \\ 60\cdot\sin ((360)/(120)) \\ 60\cdot\sin (3) \\ 60\cdot0.0523 \\ 3.138 \end{gathered}`

We can then calculate the difference with π using a calculator as:

`|3.138-\pi|=0.0036`

The difference is approximately 0.0036.