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Question Number 171283 by cortano1 last updated on 11/Jun/22

Commented by mr W last updated on 11/Jun/22

a=2R sin 70° b=2R sin 60° c=2R sin 50° a+b+c=24 2R(sin 70°+sin 60°+sin 50°)=24 ⇒a=((24 sin 70°)/(sin 70°+sin 60°+sin 50°))=8.77 ⇒b=((24 sin 60°)/(sin 70°+sin 60°+sin 50°))=8.08 ⇒c=((24 sin 50°)/(sin 70°+sin 60°+sin 50°))=7.15

$${a}=\mathrm{2}{R}\:\mathrm{sin}\:\mathrm{70}° \\ $$$${b}=\mathrm{2}{R}\:\mathrm{sin}\:\mathrm{60}° \\ $$$${c}=\mathrm{2}{R}\:\mathrm{sin}\:\mathrm{50}° \\ $$$${a}+{b}+{c}=\mathrm{24} \\ $$$$\mathrm{2}{R}\left(\mathrm{sin}\:\mathrm{70}°+\mathrm{sin}\:\mathrm{60}°+\mathrm{sin}\:\mathrm{50}°\right)=\mathrm{24} \\ $$$$\Rightarrow{a}=\frac{\mathrm{24}\:\mathrm{sin}\:\mathrm{70}°}{\mathrm{sin}\:\mathrm{70}°+\mathrm{sin}\:\mathrm{60}°+\mathrm{sin}\:\mathrm{50}°}=\mathrm{8}.\mathrm{77} \\ $$$$\Rightarrow{b}=\frac{\mathrm{24}\:\mathrm{sin}\:\mathrm{60}°}{\mathrm{sin}\:\mathrm{70}°+\mathrm{sin}\:\mathrm{60}°+\mathrm{sin}\:\mathrm{50}°}=\mathrm{8}.\mathrm{08} \\ $$$$\Rightarrow{c}=\frac{\mathrm{24}\:\mathrm{sin}\:\mathrm{50}°}{\mathrm{sin}\:\mathrm{70}°+\mathrm{sin}\:\mathrm{60}°+\mathrm{sin}\:\mathrm{50}°}=\mathrm{7}.\mathrm{15} \\ $$

Commented by SLVR last updated on 11/Jun/22

Great sir..Nice

$${Great}\:{sir}..{Nice} \\ $$

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