Trig Problem #6

trig6.jpg (17280 bytes)

The drawing above represents a female #3 Morse taper.  It is a tapered hole that measures .938 dia. at the large end and tapers down to a dia. of .778 at the small end over a distance of 3.1875.

Suppose that a .875 dia. ball bearing was pushed into the tapered hole, and a measurement was taken from the face of the hole to the ball. (Dimension X in the drawing.)

Solve for dimension X.

(If you were boring such a hole on the lathe this would be a very accurate way of measuring the size.  Just be sure that you can reach around the back to poke the ball bearing out before you stuff it in there.  Otherwise, you'll be S O L.)