Question

Dois lados de um triângulo medem 3cm e 8 cm e formam um ângulo de medida cx. Se a área desse triângulo é 6raiz 3 cm2

Answer 1

$Sabemos\ que:\\\\ a=3\ cm\ \ \| \ \ b=8\ cm\\ A=6\sqrt{3}\ cm^2 \ \ \| \ \ A=\frac{a.b.sin\ x}{2}\\\\ Calculando\ sin\ x: \\\\ 6\sqrt{3}=\frac{3.8.sin\ x}{2}\\\\ 12\sqrt{3}= 24.sin\ x\\\\ sin\ x= \frac{12\sqrt{3}}{24}\\\\ sin\ x= \frac{\sqrt{3}}{2}\ --\ \textgreater \ \ \| \ x=60^o\ \| \\\\ Calculando\ o\ valor\ de\ c:\\\\ c^2=a^2+b^2-2.a.b.cos\ x\\ c^2=3^2+8^2-2.3.8.\frac{1}{2}\\ c^2=9+64-3.8\\ c^2=73-24\\ c^2=49\\ c=\sqrt{49}\ --\ \textgreater \ \ \| \ c=7\ cm\ \|$