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Problem $13\mathrm{.}005-$ Pitch diameters, pitch angles and face width of a bevel pinion

A $20$ straight$-$tooth bevel pinion having $14$ teeth and a diametral pitch of $5$ teeth$/$in drives a $31-$tooth gear. The two shafts are at right angles and in the same plane.

Problem $13\mathrm{.}005.$c $-$ Face width

Determine the face width. $($Round the final answer to three decimal places.$)$

The face width is $$ in$.$