Question

Num triângulo ABC são dados:
A= 60 graus
B=45 graus
e BC= 4 cm
Determine a medida de AC

Answer 1

lei dos senos
x/sen 45 = 4/sen 60
x/raiz de dois sobre 2 = 4/raiz de tres sobre 3
4 raiz de dois = x raiz de tres
x= 4 raiz de 2/ raiz de tres
x = (4 raiz de 6 sobre 3) cm

Answer 2

Valor de AC > 4√6/3

Temos que aplicar a Lei dos senos

$\large \sf \boxed{\sf \dfrac{a}{sen \hat{A} } = \dfrac{b}{sen \hat{B} } = \dfrac{c}{sen \hat{C}} = 2R }$

Temos que ângulo A vale 60° e ângulo B vale 45. Aplicamos a lei dos senos:

$\Large \sf \dfrac{x}{sen 45} = \dfrac{4}{sen 60} \Rightarrow \dfrac{x}{\sqrt{2}/2} = \dfrac{4}{\sqrt{3}/2} \\\\ \Large \boxed{\begin{array}{c} \\\sf x\dfrac{\sqrt{3}}{2} = \dfrac{4\sqrt{2}}{2} \\\\\sf x = \dfrac{4\sqrt{2}}{\sqrt{3}} \\\\\sf x = \dfrac{4\sqrt{6}}{3} \\\:\end{array}}$

❄️Resposta:

$\huge \boxed{\boxed{\sf x = \dfrac{4\sqrt{6}}{3}}}$

$\huge\text{\sf -----------\ \sf\small\LaTeX\ \,\huge-----------}$

$\Large \boxed{ \boxed{ \mathbb{\displaystyle\sum}\sf{uri}\tt{lo}\bf{G\Delta}}}$