2007-05-23 15:58:54 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
radius = 6.85*tan(75 deg) = 25.56454803 inches
2007-05-23 16:13:22 · answer #1 · answered by Anonymous · 0⤊ 0⤋
it involves some simple trigonometry. If you draw the radius of the circle, it will be perpendicular to a side and also bisect the side (making each half of a side 164.4/12 / 2 = 6.85 in.). One isosceles triangle within the dodecagon has a vertex angle of 360°/12 = 30°, and the radius of the circle bisects that angle for 15°. So you set up a little equation to solve for the radius of the circle.
tan 15° = 6.85 / r --> r = 6.85/tan15° = 25.56 inches
2007-05-23 23:39:52 · answer #2 · answered by Kathleen K 7 · 0⤊ 0⤋
s = 164.4/12 = 13.7
θ = 360/12 = 30°
r = (s/2)/tan(θ/2)
r = 6.85/tan15°
r = 25.56455 in.
2007-05-23 23:12:09 · answer #3 · answered by Helmut 7 · 0⤊ 0⤋
Find the side, then find the central angle (360/12)
THEN put them in this formula: the side length divided by 2*Sin1/2central angle. Good luck!
2007-05-23 23:11:29 · answer #4 · answered by animalover 4 · 0⤊ 0⤋
25.564548 units for a radius
with an area of 2101.4058 square unites
2007-05-23 23:06:53 · answer #5 · answered by Anonymous · 1⤊ 0⤋
I have no idea.
2007-05-23 23:06:33 · answer #6 · answered by John C 2 · 0⤊ 2⤋