Question

Preciso de ajuda!!!!

Answer 1

Explicação passo-a-passo:

Usando a lei dos senos:

$\frac{a}{senA} =\frac{b}{senB}=\frac{c}{senC}$

a)Temos que A=60°, C=45°, a=$3\sqrt{2} cm$ e c=x.

$\frac{a}{senA} =\frac{c}{senC}\\\\\frac{3\sqrt{2} }{sen60} =\frac{x}{sen45}\\\\\frac{3.\sqrt{2} }{\frac{\sqrt{3} }{2} } =\frac{x}{\frac{\sqrt{2} }{2} }\\\\\frac{\sqrt{3} }{2}.x=3.\sqrt{2} .\frac{\sqrt{2} }{2}\\\\\frac{\sqrt{3} }{2}.x=3.\frac{2}{2} \\\\\frac{\sqrt{3} }{2}.x=3\\\\x=\frac{6}{\sqrt{3} } .\frac{\sqrt{3}}{\sqrt{3}} =\frac{6.\sqrt{3}}{3} \\\\x=2\sqrt{3} cm$

b)Temos que A=30°, B=45°, a=x, b=8cm

$\frac{a}{senA} =\frac{b}{senB}}$

$\frac{x}{sen30} =\frac{8}{sen45}\\\\\frac{x}{\frac{1}{2} } =\frac{8}{\frac{\sqrt{2} }{2}}\\\\x.\frac{\sqrt{2} }{2}=8.\frac{1}{2} \\\\x.\frac{\sqrt{2} }{2}=4\\\\x=\frac{8}{\sqrt{2} } .\frac{\sqrt{2}}{\sqrt{2}} =\frac{8\sqrt{2}}{2} \\\\x=4\sqrt{2}cm$