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Question Number 186883 by Mingma last updated on 11/Feb/23

Answered by HeferH last updated on 12/Feb/23

Commented by HeferH last updated on 12/Feb/23

Commented by Mingma last updated on 12/Feb/23

Great

Answered by mr W last updated on 12/Feb/23

Commented by mr W last updated on 12/Feb/23

$$AC=\frac{\sin 135a}{\sin \theta }$$$$AC=\frac{\sin 75\sqrt{2}a}{\sin (75+\theta )}$$$$\frac{\sin (75+\theta )}{\sqrt{2}\sin 75}=\frac{\sin \theta }{\sin 135}$$$$(2-\sqrt{3})\sin \theta +\cos \theta =2\sin \theta$$$$\tan \theta =\frac{1}{\sqrt{3}}\Rightarrow \theta =30°$$$$\mathrm{\angle }ACB=180-30-75=75=\mathrm{\angle }ABC$$$$\Rightarrow AC=AB$$

Commented by Mingma last updated on 12/Feb/23

Nice work!

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