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Question-176716




Question Number 176716 by cortano1 last updated on 25/Sep/22
Answered by mr W last updated on 26/Sep/22
Commented by Tawa11 last updated on 26/Sep/22
Great sir
$$\mathrm{Great}\:\mathrm{sir} \\ $$
Commented by mr W last updated on 26/Sep/22
β+30°+α+120°=180°  ⇒β=30°−α  ((sin 2α)/( (√3)))=((sin β)/1)=((sin (30°−α))/1)  sin 2α=(√3) sin (30°−α)  ⇒α≈14.1328° ⇒∠ABC≈45.8672°
$$\beta+\mathrm{30}°+\alpha+\mathrm{120}°=\mathrm{180}° \\ $$$$\Rightarrow\beta=\mathrm{30}°−\alpha \\ $$$$\frac{\mathrm{sin}\:\mathrm{2}\alpha}{\:\sqrt{\mathrm{3}}}=\frac{\mathrm{sin}\:\beta}{\mathrm{1}}=\frac{\mathrm{sin}\:\left(\mathrm{30}°−\alpha\right)}{\mathrm{1}} \\ $$$$\mathrm{sin}\:\mathrm{2}\alpha=\sqrt{\mathrm{3}}\:\mathrm{sin}\:\left(\mathrm{30}°−\alpha\right) \\ $$$$\Rightarrow\alpha\approx\mathrm{14}.\mathrm{1328}°\:\Rightarrow\angle{ABC}\approx\mathrm{45}.\mathrm{8672}° \\ $$

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