Question

no triangulo ABC determine o valor de X.​

Answer 1

• Para determinar o valor de x podemos utilizar a Lei dos senos;

$\green{\boxed{\sf \purple{\boxed{\sf \frac{a}{sen \alpha } = \frac{b}{sen \beta } }}}} \\ \\ \frac{x}{sen60} = \frac{8}{sen45} \\ \\ \frac{x}{ \frac{ \sqrt{3} }{2} } = \frac{8}{ \frac{ \sqrt{2} }{2} } \\ \\ \frac{ \sqrt{2} }{2} \times x = 8 \times \frac{ \sqrt{3} }{2} \\ \\ \frac{ \sqrt{2} }{2} x = 4 \sqrt{3} \\ \\ \sqrt{2} x = 2 \times 4 \sqrt{3} \\ \sqrt{2x} = 8 \sqrt{3} \\ x = \frac{8 \sqrt{3} } { \sqrt{2} } \: \: \: \times \frac{ \sqrt{2} }{ \sqrt{2} } \\ \\ x = \frac{8 \sqrt{6} }{ \sqrt{4} } \\ \\ x = \frac{8 \sqrt{6} }{2} \\ \\ \green{\boxed{\sf \purple{\boxed{\sf x = 4 \sqrt{6} cm}}}}$

espero ter ajudado!