Question Number 72247 by TawaTawa last updated on 26/Oct/19
Answered by mind is power last updated on 26/Oct/19
$$\mathrm{s}_{\mathrm{1}} =\mathrm{s}_{\mathrm{2}} =\mathrm{s} \\ $$$$\frac{\mathrm{TS}}{\mathrm{PR}}=\frac{\mathrm{QT}}{\mathrm{QP}}\Rightarrow\mathrm{TS}=\frac{\mathrm{41}}{\mathrm{3}} \\ $$$$\mathrm{a}=\angle\mathrm{QST}\:,\mathrm{r}=\angle\mathrm{QST}=\angle\mathrm{PRQ} \\ $$$$\frac{\mathrm{SQ}}{\mathrm{sin}\left(\mathrm{a}\right)}=\frac{\mathrm{14}}{\mathrm{sin}\left(\mathrm{R}\right)} \\ $$$$\frac{\mathrm{28}}{\mathrm{sin}\left(\mathrm{s}\right)}=\frac{\mathrm{ps}}{\mathrm{sin}\left(\mathrm{a}\right)} \\ $$$$\frac{\mathrm{PS}}{\mathrm{sin}\left(\mathrm{R}\right)}=\frac{\mathrm{41}}{\mathrm{sin}\left(\mathrm{s}\right)}\Rightarrow\mathrm{41sin}\left(\mathrm{r}\right)=\mathrm{28sin}\left(\mathrm{a}\right) \\ $$$$\frac{\mathrm{SQ}}{\mathrm{sin}\left(\mathrm{a}\right)}=\frac{\mathrm{14}}{\mathrm{sin}\left(\mathrm{r}\right)}\Rightarrow\mathrm{SQ}=\frac{\mathrm{14sin}\left(\mathrm{r}\right)}{\mathrm{sin}\left(\mathrm{a}\right)}=\mathrm{14}\frac{\mathrm{28}}{\mathrm{41}}=\frac{\mathrm{392}}{\mathrm{41}} \\ $$$$ \\ $$
Commented by TawaTawa last updated on 27/Oct/19
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{I}\:\mathrm{appreciate} \\ $$
Commented by mind is power last updated on 27/Oct/19
$$\mathrm{y},\mathrm{re}\:\mathrm{welcom} \\ $$