I have tried setting up this problem using right triangles but have not been able to solve it correctly. This problem is not as simple as it looks. It cannot be assumed that the bottom of the circle is tangent to a line drawn across the bottom. Solving for that one triangle is part of the solution.
Theta is given as 20 degrees and the book supplies the answer as 0.69341. The answer is not 0.625.
A distance in a gage is found using trigonometric formulas on triangles and circles. The solution is detailed and is correct.