The force vector vec$(F)$ has a magnitude of $F=490lb$ and acts at point $A$ at an angle $B=8\mathrm{.}3$ with respect

to vertical as shown. The force vec$(F)$ is balanced by the tension forces parallel to the two rods $AC$ and $AB$

such that the vector equation vec$(F)+$vec$(F{)}_{AC}+$vec$(F{)}_{AB}=0$ is satisfied. Determine the tension forces in the two

rods in Cartesian components.

Values for dimensions on the figure are given in the following table. Note the figure may not be to scale.

Variable Value

$a,4\mathrm{.}9ft$

$b,2\mathrm{.}1ft$

$c,3\mathrm{.}1ft$

For the component notation, use an $\text{'}xy\text{'}$ coordinate system with $y\text{'}$ poining up and $\text{'}x\text{'}$ pointing to the right.

vec$(F{)}_{AC}=1,$hat$(3^{})+$

$)$ Ib

vec$(F{)}_{AB}=$

hat$(3)+$

$)$ lb