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Question Number 139545 by aliibrahim1 last updated on 28/Apr/21

Answered by mr W last updated on 28/Apr/21

Commented by mr W last updated on 28/Apr/21

((sin α)/(sin 48))=((sin (54−α))/(sin 66))=((sin 54 cos α−cos 54 sin α)/(sin 66)) tan α=((sin 54)/(((sin 66)/(sin 48))+cos 54))⇒α=24°

$$\frac{\mathrm{sin}\:\alpha}{\mathrm{sin}\:\mathrm{48}}=\frac{\mathrm{sin}\:\left(\mathrm{54}−\alpha\right)}{\mathrm{sin}\:\mathrm{66}}=\frac{\mathrm{sin}\:\mathrm{54}\:\mathrm{cos}\:\alpha−\mathrm{cos}\:\mathrm{54}\:\mathrm{sin}\:\alpha}{\mathrm{sin}\:\mathrm{66}} \\ $$$$\mathrm{tan}\:\alpha=\frac{\mathrm{sin}\:\mathrm{54}}{\frac{\mathrm{sin}\:\mathrm{66}}{\mathrm{sin}\:\mathrm{48}}+\mathrm{cos}\:\mathrm{54}}\Rightarrow\alpha=\mathrm{24}° \\ $$

Commented by aliibrahim1 last updated on 28/Apr/21

thx good sir

$${thx}\:{good}\:{sir} \\ $$

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