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Question Number 190565 by cherokeesay last updated on 06/Apr/23

Answered by mr W last updated on 06/Apr/23

((CB)/(sin x))=((AC)/(sin 30°)) ...(i) ((sin (x+30°))/(CB))=((sin (x+60°))/(DB)) ...(ii) (i)×(ii): ((sin (x+30°))/(sin x))=((sin (x+60°))/(sin 30°)) ⇒x=24° or 96°

$$\frac{{CB}}{\mathrm{sin}\:{x}}=\frac{{AC}}{\mathrm{sin}\:\mathrm{30}°}\:\:\:...\left({i}\right) \\ $$$$\frac{\mathrm{sin}\:\left({x}+\mathrm{30}°\right)}{{CB}}=\frac{\mathrm{sin}\:\left({x}+\mathrm{60}°\right)}{{DB}}\:\:\:...\left({ii}\right) \\ $$$$\left({i}\right)×\left({ii}\right): \\ $$$$\frac{\mathrm{sin}\:\left({x}+\mathrm{30}°\right)}{\mathrm{sin}\:{x}}=\frac{\mathrm{sin}\:\left({x}+\mathrm{60}°\right)}{\mathrm{sin}\:\mathrm{30}°} \\ $$$$\Rightarrow{x}=\mathrm{24}°\:{or}\:\mathrm{96}° \\ $$

Commented by mr W last updated on 06/Apr/23

Commented by mr W last updated on 06/Apr/23

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