SOLUTION: In order to seal an oil pipeline, a steel flange is placed on the open end of the pipe. The flange is circular with radius 6 inches, and must have 7 holes drilled in it. These hole

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Question 731560: In order to seal an oil pipeline, a steel flange is placed on the open end of the pipe. The flange is circular with radius 6 inches, and must have 7 holes drilled in it. These holes must be 3/16 inch in diameter, they must be equally spaced apart, and their centers must be 1 inch from the perimeter of the plate.
a. Draw an accurate sketch of the flange.
b. What should be the distance between the centers of two adjacent holes? Industry standards require an answer accurate to one ten-thousandth of an inch.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The central angle A measures 360%5Eo%2F7 (or 2pi%2F7 in radians)
The ceter of the flange and two adjacent holes form an isosceles triangle, like the green one in the drawing.
The legs of such a triangle measure
6-1=5 inches.
That is the radius of the flange, 6 inches, minus the 1 inch distance from the whole to the edge of the plate.
According to the law of cosines, if the sides of a triangle with lengths b and c form an angle A, the length of the third side, opposite angle A, is given by
a=sqrt%28b%5E2%2Bc%5E2-2%2Ab%2Ac%2Acos%28A%29%29
In this case b=c=5 inches, A=2pi%2F7=360%5Eo%2F7 and a is the distance between the centers of adjacent holes. Substituting:
a=sqrt%285%5E2%2B5%5E2-2%2A5%2A5%2Acos%28A%29%29
a=sqrt%2825%2B25-50%2Acos%282pi%2F7%29%29
a=sqrt%2850-50%2Acos%282pi%2F7%29%29
a = 4.338837.... = highlight%284.3388%29 (rounded to 1%2F10000 inch)