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Question Number 67849 by mr W last updated on 01/Sep/19

Commented by MJS last updated on 01/Sep/19

$$\mathrm{is}\mathrm{the}\mathrm{angle}\mathrm{in}\mathrm{the}\mathrm{center}90°?$$

Commented by mr W last updated on 01/Sep/19

$$notgiven.$$

Commented by Prithwish sen last updated on 01/Sep/19

Commented by Prithwish sen last updated on 01/Sep/19

$$\frac{1}{2}\mathrm{absin}\alpha =3...\left(\mathrm{i}\right)$$$$\frac{1}{2}\mathrm{cdsin}\alpha =2....\left(\mathrm{ii}\right)$$$$\frac{1}{2}\mathrm{bdsin}\beta =1...\left(\mathrm{iii}\right)$$$$\mathrm{find}\frac{1}{2}\mathrm{acsin}\beta$$

Commented by MJS last updated on 01/Sep/19

$$\sin \beta =\sin \alpha$$

Commented by mr W last updated on 01/Sep/19

$$thankssirs!$$$$iusedthesamemethod.$$

Commented by Prithwish sen last updated on 01/Sep/19

$$\mathrm{thank}\mathrm{you}\mathrm{alot}.$$

Answered by mr W last updated on 01/Sep/19

Commented by mr W last updated on 01/Sep/19

$$\beta =\pi -\alpha$$$$\sin \beta =\sin \alpha =\lambda$$$$\frac{1}{2}ab\lambda =1...\left(i\right)$$$$\frac{1}{2}bc\lambda =3...\left(ii\right)$$$$\frac{1}{2}cd\lambda =x...\left(iii\right)$$$$\frac{1}{2}da\lambda =2...\left(iv\right)$$$$\left(i\right)\times \left(iii\right):\frac{abcd{\lambda }^2}{4}=1\times x$$$$\left(ii\right)\times \left(iv\right):\frac{abcd{\lambda }^2}{4}=3\times 2$$$$\Rightarrow 1\times x=3\times 2$$$$\Rightarrow x=6$$

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