Question 423148
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:
{{{A/sin(A) = B/sin(B)}}} Here B is the radius of the circle and angle B is 75 deg.
{{{A = sin(A)/sin(B)*B = sin(30)/sin(75)*(35/2)}}}
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.