${?}^{\text{D}\text{P}\text{r}\text{o}\text{b}\text{.}2\mathrm{.}8-15.\text{A}\text{t}\text{h}\text{r}\text{e}\text{e}-\text{b}\text{a}\text{r}\text{,}\text{p}\text{i}\text{n}-\text{j}\text{o}\text{i}\text{n}\text{t}\text{e}\text{d}\text{,}\text{p}\text{l}\text{a}\text{n}\text{a}\text{r}\text{t}\text{r}\text{u}\text{s}\text{s}}$

supports a single horizontal load $P$ at joint $B.$ Joint $C$ is

free to move horizontally. The allowable stress in tension is

$({}_T{)}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=140$MPa, and the allowable stress in compression

is $({}_C{)}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=-90$MPa. If the truss is to support a maximum

load $P_{\text{a}\text{l}\text{l}\text{o}\text{w}}=50kN,$ what are the required cross$-$sectional

areas, $A_i,$ of the three truss members?