Question Number 174963 by MikeH last updated on 14/Aug/22
Commented by thfchristopher last updated on 15/Aug/22
$$\mathrm{But}\:\mathrm{there}\:\mathrm{is}\:\mathrm{no}\:\mathrm{such}\:\mathrm{option}\:\mathrm{for}\:\mathrm{7}.\mathrm{31}... \\ $$
Answered by a.lgnaoui last updated on 15/Aug/22
$$\mathrm{7},\mathrm{31} \\ $$
Answered by behi834171 last updated on 15/Aug/22
$${XY}={b} \\ $$$$\Rightarrow{XZ}^{\mathrm{2}} ={XY}^{\mathrm{2}} +{YZ}^{\mathrm{2}} −\mathrm{2}{XY}.{YZ}.\boldsymbol{{cos}}\overset{ } {\boldsymbol{{Y}}} \\ $$$$\Rightarrow\mathrm{5}^{\mathrm{2}} ={b}^{\mathrm{2}} +{b}^{\mathrm{2}} −\mathrm{2}{b}^{\mathrm{2}} {cos}\mathrm{40}\Rightarrow \\ $$$$\Rightarrow\boldsymbol{{b}}^{\mathrm{2}} =\frac{\mathrm{25}}{\mathrm{2}\left(\mathrm{1}−\boldsymbol{{cos}}\mathrm{40}\right)}\Rightarrow\:\:\:\:\boldsymbol{{b}}=\mathrm{7}.\mathrm{31}\:\:.\blacksquare \\ $$
Commented by MikeH last updated on 15/Aug/22
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{I}\:\mathrm{solved}\:\mathrm{that}\:\mathrm{and}\:\mathrm{I}\:\mathrm{was}\:\mathrm{shock}\: \\ $$$$\mathrm{that}\:\mathrm{I}\:\mathrm{was}\:\mathrm{wrong} \\ $$
Answered by mr W last updated on 15/Aug/22
$${XY}=\frac{\mathrm{5}}{\mathrm{2}\:\mathrm{sin}\:\frac{\mathrm{40}°}{\mathrm{2}}}\approx\mathrm{7}.\mathrm{31} \\ $$