SOLUTION: I have a 24 foot pool inside a deck. I want to put a border around the pool using 1X6 boards. There are 16 sides and 16 angles. How long to I cut each side and at what angle to I c

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: I have a 24 foot pool inside a deck. I want to put a border around the pool using 1X6 boards. There are 16 sides and 16 angles. How long to I cut each side and at what angle to I c      Log On

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Question 990884: I have a 24 foot pool inside a deck. I want to put a border around the pool using 1X6 boards. There are 16 sides and 16 angles. How long to I cut each side and at what angle to I cut the boards? I tried 360/16 and got 22.5, but when I cut the boards at that angle, it was incorrect.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
You want to put a 16-sided regular polygonal {Hexadecagonal) deck
around a 24 foot circular pool.
.
The angle between sides,x (interior angle):(n=number of sides=16)
x=%28%28n-2%29%2Fn%29+%2A+180
x=%28%2816-2%29%2F16%29%2A180
x=%2814%2F16%29%2A180
x=157.5 The angle to cut is 1/2 this angle.
ANSWER 1: The angle to cut is 78.75 degrees (both ends).
.
For each side tangent to a 24 foot circle:
(each side of the deck will touch the pool at its midpoint)
.
a=side length; r=radius=12 feet
.
a=2rtan%28180%2Fn%29
a=2%2812ft%29tan%28180%2F16%29
a=24ft%280.1989%29
a=4.77ft
ANSWER 2:The side length is 4 feet 9 and 1/4 inch.