I am trying to solve the bend angle for a bar given specific dimensions. The bend angle is acute as in the bar traverses the pin for more than 90-degrees. The bend angle is the angle of the projected lines from the 2 tangents of the pin.

I'm given the diameter of the pin, and the diameter of the bar. I am also given the out-to-out dimensions of the leg that traverses the pin.

Because the bar has thickness calculating this angle does not give us the bend angle. We are calculating the height to the top corner of the bar and the length to the outside corner of the bar.

From what I have how do I get the bend angle? The accompanying link has a picture. I'm trying to find Angle E given the green line, yellow pin and bar diameter.

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I'm not sure if I can solve with the information given but think I should be able to.

I thought maybe I could solve using some sort of combination of slope-intercept and circle equation but I think I don't have enough information.

I know how have 2 lines with the same slope. I know the y-coordinate of the given hypotenuse matches the y-coordinate of the top outside bar and the x-coordinate of the given hypotenuse matches the x-coordinate of the lower inside bar.

I know I could solve it if the end point of the hypotenuse match either corner (point) of the bar. I know there are plenty of right angles to be made but none that share a side with one I already know.

This may be a bit confusing and I apologize. If you need more clarification please let me know. Thank you for your help.