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Question Number 72247 by TawaTawa last updated on 26/Oct/19

Answered by mind is power last updated on 26/Oct/19

$${\mathrm{s}}_1={\mathrm{s}}_2=\mathrm{s}$$$$\frac{\mathrm{TS}}{\mathrm{PR}}=\frac{\mathrm{QT}}{\mathrm{QP}}\Rightarrow \mathrm{TS}=\frac{41}{3}$$$$\mathrm{a}=\mathrm{\angle }\mathrm{QST},\mathrm{r}=\mathrm{\angle }\mathrm{QST}=\mathrm{\angle }\mathrm{PRQ}$$$$\frac{\mathrm{SQ}}{\sin \left(\mathrm{a}\right)}=\frac{14}{\sin \left(\mathrm{R}\right)}$$$$\frac{28}{\sin \left(\mathrm{s}\right)}=\frac{\mathrm{ps}}{\sin \left(\mathrm{a}\right)}$$$$\frac{\mathrm{PS}}{\sin \left(\mathrm{R}\right)}=\frac{41}{\sin \left(\mathrm{s}\right)}\Rightarrow 41\sin \left(\mathrm{r}\right)=28\sin \left(\mathrm{a}\right)$$$$\frac{\mathrm{SQ}}{\sin \left(\mathrm{a}\right)}=\frac{14}{\sin \left(\mathrm{r}\right)}\Rightarrow \mathrm{SQ}=\frac{14\sin \left(\mathrm{r}\right)}{\sin \left(\mathrm{a}\right)}=14\frac{28}{41}=\frac{392}{41}$$$$$$

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

$$\mathrm{y},\mathrm{re}\mathrm{welcom}$$

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