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Resolvendo utilizando a lei dos cossenos:
![a^2=b^2+c^2-2.b.c. \cos \^A\\\\\\\\
a)\\\\\
x^2=10^2+16^2-2.(10).(16). \cos 60^o\\\\
x^2=356-160\\\\
x=\pm\sqrt{196}\ (utilizando\ apenas\ o\ valor\ positivo)\\\\
\boxed{x=14\ cm}\\\\\\\\
b)\\\\\
x^2=(3\sqrt{2})^2+7^2-2.(3\sqrt{2}).(7). \cos 45^o\\\\
x^2=(3^2\sqrt{2}^2)+49-42\sqrt{2}. \dfrac{\sqrt{2}}{2}\\\\
x^2=18+49-42\\\\
x=\pm\sqrt{25}\ (utilizando\ apenas\ o\ valor\ positivo)\\\\
\boxed{x=5\ cm}](https://tex.z-dn.net/?f=a%5E2%3Db%5E2%2Bc%5E2-2.b.c.+%5Ccos+%5C%5EA%5C%5C%5C%5C%5C%5C%5C%5C%0Aa%29%5C%5C%5C%5C%5C%0Ax%5E2%3D10%5E2%2B16%5E2-2.%2810%29.%2816%29.+%5Ccos+60%5Eo%5C%5C%5C%5C%0Ax%5E2%3D356-160%5C%5C%5C%5C%0Ax%3D%5Cpm%5Csqrt%7B196%7D%5C+%28utilizando%5C+apenas%5C+o%5C+valor%5C+positivo%29%5C%5C%5C%5C%0A%5Cboxed%7Bx%3D14%5C+cm%7D%5C%5C%5C%5C%5C%5C%5C%5C%0Ab%29%5C%5C%5C%5C%5C%0Ax%5E2%3D%283%5Csqrt%7B2%7D%29%5E2%2B7%5E2-2.%283%5Csqrt%7B2%7D%29.%287%29.+%5Ccos+45%5Eo%5C%5C%5C%5C%0Ax%5E2%3D%283%5E2%5Csqrt%7B2%7D%5E2%29%2B49-42%5Csqrt%7B2%7D.+%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5C%5C%5C%5C%0Ax%5E2%3D18%2B49-42%5C%5C%5C%5C%0Ax%3D%5Cpm%5Csqrt%7B25%7D%5C+%28utilizando%5C+apenas%5C+o%5C+valor%5C+positivo%29%5C%5C%5C%5C%0A%5Cboxed%7Bx%3D5%5C+cm%7D "a^2=b^2+c^2-2.b.c. \cos \^A\\\\\\\\
a)\\\\\
x^2=10^2+16^2-2.(10).(16). \cos 60^o\\\\
x^2=356-160\\\\
x=\pm\sqrt{196}\ (utilizando\ apenas\ o\ valor\ positivo)\\\\
\boxed{x=14\ cm}\\\\\\\\
b)\\\\\
x^2=(3\sqrt{2})^2+7^2-2.(3\sqrt{2}).(7). \cos 45^o\\\\
x^2=(3^2\sqrt{2}^2)+49-42\sqrt{2}. \dfrac{\sqrt{2}}{2}\\\\
x^2=18+49-42\\\\
x=\pm\sqrt{25}\ (utilizando\ apenas\ o\ valor\ positivo)\\\\
\boxed{x=5\ cm}")
Espero ter ajudado.
Bons estudos!
Espero ter ajudado.
Bons estudos!
ScreenBlack:
Obrigado pela melhor resposta :)
Mais que merecido ;)
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