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Question Number 57296 by mr W last updated on 01/Apr/19

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

$$Findx=?$$

Answered by MJS last updated on 02/Apr/19

$$A=\left(\begin{array}{c}-a\\ 0\end{array}\right)B=\left(\begin{array}{c}0\\ 0\end{array}\right)C=\left(\begin{array}{c}-b\cos 40°\\ b\sin 40°\end{array}\right)D=\left(\begin{array}{c}-b\cos 20°\\ b\sin 20°\end{array}\right)$$$$\mathrm{line}AD:\mathfrak{y}=\frac{b\sin 20°}{a-b\cos 20°}\mathfrak{x}+\frac{ab\sin 20°}{a-b\cos 20°}\Rightarrow$$$$\Rightarrow x=40°-\arctan \frac{b\sin 20°}{a-b\cos 20°}$$$$a=b\frac{\sin 100°}{\sin 40°}$$$$x=40°-\arctan \frac{\sqrt{3}}{3}=10°$$

Commented by mr W last updated on 02/Apr/19

$$thankssir!iguesseditmustbe10°.$$$$i^{\prime }llseeifthereisapurelygeometrical$$$$waytogetthesameresult.$$

Commented by MJS last updated on 02/Apr/19

$${\mathrm{I}}^{\prime }\mathrm{m}\mathrm{always}\mathrm{fast}\mathrm{with}\mathrm{coordinates},\mathrm{but}\mathrm{there}$$$$\mathrm{should}\mathrm{be}\mathrm{other}\mathrm{possibilities}...$$

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