The traffic light shown in $($Figure $1)$ has a mass of$19$ kg

$.$ Take h

$=3\mathrm{.}5$ m

$.$

Figure$1$ of $1$

Traffic light A supported by cables AB$,$ AC$,$ and AD is shown in the xyz space with the z$-$axis directed upward. Ends B$,$ C$,$ and D of the cables are attached to top ends of three vertical poles. The traffic light is located on the positive z$-$axis at distance h from the xy plane. End B of cable AB is located in the $+$x$+$y$+$z octant, $4$ meters above the xy plane, $3$ meters from the yz plane, and $4$ meters from the xz plane. End C of cable AC is located in the $-$x$-$y$+$z octant, $6$ meters above the xy plane, $6$ meters from the yz plane, and $3$ meters from the xz plane. End D of cable AD is located in the $+$x$-$y$+$z octant $4$ meters above the xy plane, $4$ meters from yz plane, and $3$ meters from the xz plane.

Part A

Determine the tension developed in the cable AB

required to support the traffic light