Question

qual a distância entre os pontos A e B no triângulo abaixo?

Answer 1

$Ola'~~~\mathbf{Mayra} \\ \\ O~\^angulo~(C)~e'~ 60\°~pela~soma~dos~\^angulos~internos~ \\ Da~figura~por~lei~de~senos~temos: \\ \\ \frac{AB}{sen60\°}= \frac{BC}{sen45\° } \\ \\ \frac{AB}{sen60\°}= \frac{20}{sen45\°}~~--\ \textgreater \ sabemos~que~\begin{cases}sen60\°= \frac{ \sqrt{3} }{2} \\ sen45\°= \frac{ \sqrt{2} }{2} \end{cases} \\ \\ AB= \frac{20(sen60\°)}{sen45\° } \\ \\ AB= \frac{20( \frac{ \sqrt{3} }{2} )}{ \frac{ \sqrt{2} }{2} } \\ \\ \boxed{\boxed{AB=10 \sqrt{6} }}$

$alternativa~\textcircled{e} \\ \\ \mathbb{ttttttttttttttttttttttttttttttttttttttt}\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~ter~ajudado!!$