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| Math Central | Quandaries & Queries |
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Need to lay out a 10 ft. diameter octagon on the ground. What is the length of the sides ? And the angles ? Thanks , Frank |
Hi Frank,
I think the angle you need is the angle ABC which measures 67.5 degrees.
Suppose the side length AB is s feet. I'm not sure which distance is 10 feet.
If it is the distance from A to E then as Stephen showed s is 0.4142 times the distance from A to E so
s = 4.142 feet.
If the distance from A to D is 10 feet then since triangle AED is a right triangle we can use Pythagoras' theorem to find s. |ED| = 1/0.4142 s and |ED| = s so
|AD|2 = 1/0.41422 s2 + s2
and hence
102 = (3.4142)s2.
Thus
s2 = 100/3.4142
and
s = 5.41 feet
I hope this helps,
Harley
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