SOLUTION: There are eight holes equally spaced on the flange. Find the distance between the centers of the holes.The bolt diameter is 4.5 inches.

Question 204012This question is from textbook Mathematics For Technical trades
: There are eight holes equally spaced on the flange. Find the distance between the centers of the holes.The bolt diameter is 4.5 inches. This question is from textbook Mathematics For Technical trades

Found 2 solutions by RAY100, scott8148:
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
Radius = dia /2 = 4.5/2=2.25
.
central angle is 360 /8 =45.
,
drawing a rough sketch, the median to the line between the holes,from the center if the circle, is a perpendicular bisector of that line.
.
Let d = distance of the line between holes,,then
,
sin(45/2) = (d/2) / 2.25
.
(sin 22.5)(2.25) = d/2
.
d=1.722
.
check sin a= 1.722/2/2.25 =.3827,,,a=22.5,,,,ok
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
this is either a very large flange using 4 1/2 " bolts, or a small flange with a 4.5" bolt circle ___ let's assume small

the radius of the bolt circle is 2.25" (half the diameter}

a triangle is formed by two adjacent holes and the center of the flange opening

this is an isosceles triangle with a vertex angle of 45� (1/8 of 360�) and a side length of 2.25"

the distance between centers is the base (b) of the triangle

using trigonometry ___ b/2 = 2.25 [sin(22.5�)] ___ b = 1.72" (approx)
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