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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

s_1 =s_2 =s ((TS)/(PR))=((QT)/(QP))⇒TS=((41)/3) a=∠QST ,r=∠QST=∠PRQ ((SQ)/(sin(a)))=((14)/(sin(R))) ((28)/(sin(s)))=((ps)/(sin(a))) ((PS)/(sin(R)))=((41)/(sin(s)))⇒41sin(r)=28sin(a) ((SQ)/(sin(a)))=((14)/(sin(r)))⇒SQ=((14sin(r))/(sin(a)))=14((28)/(41))=((392)/(41))

$$\mathrm{s}_{\mathrm{1}} =\mathrm{s}_{\mathrm{2}} =\mathrm{s} \\ $$$$\frac{\mathrm{TS}}{\mathrm{PR}}=\frac{\mathrm{QT}}{\mathrm{QP}}\Rightarrow\mathrm{TS}=\frac{\mathrm{41}}{\mathrm{3}} \\ $$$$\mathrm{a}=\angle\mathrm{QST}\:,\mathrm{r}=\angle\mathrm{QST}=\angle\mathrm{PRQ} \\ $$$$\frac{\mathrm{SQ}}{\mathrm{sin}\left(\mathrm{a}\right)}=\frac{\mathrm{14}}{\mathrm{sin}\left(\mathrm{R}\right)} \\ $$$$\frac{\mathrm{28}}{\mathrm{sin}\left(\mathrm{s}\right)}=\frac{\mathrm{ps}}{\mathrm{sin}\left(\mathrm{a}\right)} \\ $$$$\frac{\mathrm{PS}}{\mathrm{sin}\left(\mathrm{R}\right)}=\frac{\mathrm{41}}{\mathrm{sin}\left(\mathrm{s}\right)}\Rightarrow\mathrm{41sin}\left(\mathrm{r}\right)=\mathrm{28sin}\left(\mathrm{a}\right) \\ $$$$\frac{\mathrm{SQ}}{\mathrm{sin}\left(\mathrm{a}\right)}=\frac{\mathrm{14}}{\mathrm{sin}\left(\mathrm{r}\right)}\Rightarrow\mathrm{SQ}=\frac{\mathrm{14sin}\left(\mathrm{r}\right)}{\mathrm{sin}\left(\mathrm{a}\right)}=\mathrm{14}\frac{\mathrm{28}}{\mathrm{41}}=\frac{\mathrm{392}}{\mathrm{41}} \\ $$$$ \\ $$

Commented by TawaTawa last updated on 27/Oct/19

God bless you sir. I appreciate

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{I}\:\mathrm{appreciate} \\ $$

Commented by mind is power last updated on 27/Oct/19

y,re welcom

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

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