Problem $1\mathrm{.}6($Related Topic: Force Vectors, Position Vectors, and Vector Operations$)$

Steel framing members $AB,BC,$ and $CD$ are joined at $B$ and $C$ and are braced using cables $EF$ and $EG.$ Knowing that $E$ is at the midpoint of $BC$ and that the tension in cable $EG$ is $178$ lb $,$ determine $(a)$ the angle between $EG$ and member $BC,(b)$ the projection on $BC$ of the force exerted by cable $EG$ at point $E.$