Quandaries
and Queries
Scott
I am a parent.
The level of the question secondary (10-12)
I want to build a octagonal deck. The wood I am using are cut in 8 foot lenghts. What I want to know is if the sides of the octagonal are 8 feet, what is the diameter. Also what are the angles of each side?
Your help is greatly appreciatted.
Hi Scott,
From the diagram you can see that d = 8 + 2x feet, where d is the diameter.
Thus if you can find x then d is easy to calculate. Triangle ABC is a right triangle, so by Pythagoras' Theorem
x2 + x2 = 82 = 64
Thus
2 x2 = 64 and x2 = 32.
Thus
x = √32 = 4 √2
Thus
d = 8 + 2x = 8 + 8 √2 = 19.3137 feet
which is approximately 19 feet 3 3/4 inches.
The angle calculation you can find in the answer to a previous question.
Penny