Original Question:
I'm into building bird
feeders(see
picture ) and need to know if there is a formula to
calculate the length and the width of the pie shaped
pieces that make up the roof, I would like to keep the roof
about 16" wide and about 5" high
using 10 pie or (pyramid) shaped pieces per roof.
If you have a better or easier way to compute the sizes
I'm all ears.
Solution:
 Click
on this calculator link
to open a calculator window.
Diagram 1 is a "birds eye" view
of the bird house. The house has ten sides with radius of 8".
Angle AOB will be 36 degrees (360/10). We can calculate AB
as follows:
Bisect AOB with a perpendicuar to AB. This will also bisect
AB.
sin 18 = BC / 8 = AC / 8
BC = 8 * sin 18 = 2.4721
AB = 2 * BC = 4.9443" which will be the length of the
base of each triangle forming the roof.
Diagram 2 is the side view of the bird feeder.
OT is the inside height which was given to be 5".
The base is 8" (half the diameter given - 16")
AT2 = OA2 + OT2 = 64 + 25 = 89
AT = 9.434"
Tan (Angle AOT) = 5 / 8 thus
Angle AOT = 32 degrees
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