SOLUTION: The figure shows a circular sheet of diameter 40 centimeters. The sheet contains 12 equally spaced bolt holes. Determine the straight-line distance between the centers of the bolt

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Question 423148: The figure shows a circular sheet of diameter 40 centimeters. The sheet contains 12 equally spaced bolt holes. Determine the straight-line distance between the centers of the bolt holes.
http://www.marsd.org/15542093193535607/lib/15542093193535607/Trig_4.8.pdf
going to that link you will see the figure on page 4.
I really do not know how to try this, my book doesn't show me how to do this, my teacher hasn't showed us an example on this kind of problem, and because it's an even number question I can't even see an answer in the back of the book! So I don't know how to do this at all.
Answer by htmentor(1343) (Show Source):
You can put this solution on YOUR website!
The bolt hole centers sit on a circle of diameter 35 cm. The distance from the center of this circle to the center of each of the bolt holes is equal to the radius of this circle. Therefore, we can form a triangle with two sides equal to the radius of the circle and the third side, opposite the 30 deg. angle, is the distance between the centers of the bolt holes. The other two angles must be 75 deg. since they are equal and the sum of all 3 angles = 180 deg. We can use the following formula to determine the distance we seek:
Here B is the radius of the circle and angle B is 75 deg.

So the distance = 9.0587 cm
This answer would seem reasonable since we know that the distance of the circular arc connecting the bolt holes is s = r*theta = (35/2)*30 deg * pi rad/180 deg = 9.1630 cm, and this must be greater than the straight line distance.