Question

determine o valor de X em cada caso:

Answer 1

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$\large\boxed{\begin{array}{l}\tt a)~\sf x^2=10^2+16^2-2\cdot10\cdot16\cdot cos(60^\circ)\\\sf x^2=100+256-\diagup\!\!\!2\cdot160\cdot\dfrac{1}{\diagup\!\!\!2}\\\sf x^2=356-160\\\sf x^2=196\\\sf x=\sqrt{196}\\\sf x=14~m\end{array}}$

$\large\boxed{\begin{array}{l}\tt b)~\sf x^2=(3\sqrt{2})^2+7^2-2\cdot3\sqrt{2}\cdot7\cdot cos(45^\circ)\\\sf x^2=18+49-\diagup\!\!\!\!2\cdot21\sqrt{2}\cdot\dfrac{\sqrt{2}}{\diagup\!\!\!\!2}\\\sf x^2=67-21\cdot2\\\sf x^2=67-42\\\sf x^2=25\\\sf x=\sqrt{25}\\\sf x=5~cm\end{array}}$

$\large\boxed{\begin{array}{l}\tt c)~\sf x^2=(\sqrt{3})^2+2^2-2\cdot\sqrt{3}\cdot2\cdot cos(150^\circ)\\\sf x^2=3+4-\diagup\!\!\!\!2\cdot2\sqrt{3}\bigg(-\dfrac{\sqrt{3}}{\diagup\!\!\!\!2}\bigg)\\\sf x^2=7+6\\\sf x^2=13\\\sf x=\sqrt{13}~cm\end{array}}$