Math CentralQuandaries & Queries


Question from Tom, a parent:

Want to build a sand box for a pool that is fourteen foot round wanted to make it in fourteen pieces of wood what angle would each piece be and how long would each piece be

Hi Tom,

Have a look at my response to a similar question that Linda asked a few months ago. Her pool was 15 feet in diameter and she wanted a sand box with 8 sides. I am not sure if the 14 feet you mentioned is the diameter, if not you need to measure the diameter.

As in Linda's case you need to decide on the width of the sand box, $w$ in my diagram of Linda's pool. Look at this diagram and imagine that the sand box has 14 sides rather than the 8 shown. The dimension $L$ in the diagram is then the diameter of your pool plus $2w$ feet and hence the length $CA$ is half of $L.$

Since your sandbox has 14 sides the measure of angle $BCA$ is$ \large \frac{360}{28} = 13$ degrees. This makes the measure of the angle $ACB = 90 - 13 = 77$ degrees. This is the angle you need to cut the boards.

The tangent of the angle $BCA$ is $\large \frac{|AB|}{|CA|}$ and you know $|CA|$ and hence

\[|AB| = |CA| \tan(13) \mbox{ degrees.}\]

(Make sure your calculator is set to degrees when you find the tangent.) The length of each board is then twice $|AB|.$

I hope this helps,

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