cutting the timbers on a 22.5 degree angle how long is each timber.
2006-07-23 04:16:27 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Assuming you mean from side to side and not from corner to corner.
Join all the corner points to the center point.
All the internal angles at the center point = 360º/8 (ie 45º).
From the cent re point draw a straight line to intersect one of the sides at right angles. Now by trigonomoty:
tan Θ = Opp / Adj.
opp = Adj tan Θ
Opp = (9)(tan 22∙5) - the straight line bisects the 45º angle & opporite side.
Opp = 3.7279....
Opp(2) = 7∙4558...ft. - length of one side.
2006-07-23 04:56:51 · answer #1 · answered by Brenmore 5 · 0⤊ 0⤋
If you think of it, you have a trapezoid.
It is formed of two triangles with 45 degree angles and a rectangle with one side equal to a side of the octogon, call it x.
So: x+2*x*sqrt(2)/2 =18.
x(1+sqrt(2))=18
x= 18/2.41
x=7.456
2006-07-23 12:25:16 · answer #2 · answered by Roxi 4 · 0⤊ 0⤋
each side is 7 feet 5 1/2 inches
you take 18, divide by radical 2. 12.72
18 minus 12.72 = 5.27
5.27 X radical 2 = 7.45
2006-07-23 11:32:31 · answer #3 · answered by iberius 4 · 0⤊ 0⤋
6 ft i believe
2006-07-23 11:19:28 · answer #4 · answered by CJ I 2 · 0⤊ 0⤋
18 feet point to point or side to side?
2006-07-23 11:39:47 · answer #5 · answered by Alan Turing 5 · 0⤊ 0⤋