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I have a problem I'm trying to solve for work (we're trying to inspect a hole, and I'm trying to determine its angle using a gage pin and a ball bearing).

An image of the problem is attached. The known dimensions which we can measure are shown in black, and I am trying to solve for the angle, X. I can get a value for X by plugging this into my CAD software, butI need to know how to solve for X using hand calculationsso that the machinists can do it during production. The value for X should come out to be approximately 22 degrees. The four known dimensions, as shown, are D, H, T, and R. The part is symmetrical, and the sides of the partial cone are tangent to the circle.

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# Ball in cone issue

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