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Question Number 84970 by Power last updated on 18/Mar/20

Answered by mr W last updated on 18/Mar/20

$$2x+3y=\pi$$$$\Rightarrow x=\frac{\pi }{2}-\frac{3y}{2}$$$$\frac{AB}{\sin (x+y)}=\frac{BD}{\sin x}$$$$\Rightarrow \frac{11}{\cos \frac{y}{2}}=\frac{2}{\cos \frac{3y}{2}}$$$$\Rightarrow 11=\frac{2}{4{\cos }^2\frac{y}{2}-3}$$$$\Rightarrow {\cos }^2\frac{y}{2}=\frac{35}{44}$$$$$$$$\frac{AC}{\sin 2y}=\frac{AB}{\sin y}$$$$\Rightarrow AC=2\times AB\cos y$$$$=2\times AB(2{\cos }^2\frac{y}{2}-1)=22(\frac{70}{44}-1)=13$$

Commented by Power last updated on 18/Mar/20

$$\mathrm{thanks}$$

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