The frame ACD is hinged at A and D and is supported by a cable that passes through a ring at B and is attached to hooks at G and H$.$ Knowing that the tension in the cable is $410$ N$,$ determine the perpendicular distance between portion BH of the cable and the diagonal AD$.($Round the final answer to three decimal places.$)$

A figure shows a frame A C D in the x$-$z plane and is supported by $2$ cables attached to hooks at G and H$.$The frame is pinned to point A on the z$-$axis and point D on the x$-$axis. The cables pass through a ring at point B$.$ The coordinates, in meters, of points A$,$ D$,$ G$,$ B$,$ and H$,$ point A $(0,0,0\mathrm{.}75),$ point D $(1,0,0),$ point G $(0,0\mathrm{.}925,0\mathrm{.}35),$ point B $(0\mathrm{.}5,0,0\mathrm{.}75),$ point H $(0\mathrm{.}875,0\mathrm{.}75,0).$ Vector P acts vertically down from point C$.$

The perpendicular distance is The frame ACD is hinged at A and $D$ and is supported by a cable that passes through a ring at $B$ and is attached to hooks at $G$ and $H.$

Knowing that the tension in the cable is $410$ N $,$ determine the perpendicular distance between portion $BH$ of the cable and the

diagonal $AD.($Round the final answer to three decimal places.$)$

m $.$

m$.$