Question

Na figura abaixo, o valor de x é:

Answer 1

Resposta:

X=4√6

$180^{ \circ} = (75^{ \circ} + 60^{ \circ} + \alpha ) \\ 180^{ \circ} - 135^{ \circ} = \alpha \\ \alpha = 45^{ \circ}$

Pela lei dos senos:

$\dfrac{sen(45^{ \circ}) }{8} = \dfrac{sen(60 ^{ \circ} )}{x} \\ \\ \dfrac{ \frac{ \sqrt{2} }{2} }{8} = \dfrac{ \frac{ \sqrt{3} }{2} }{x} \\ \\ \dfrac{ \sqrt{2} }{16} = \dfrac{ \sqrt{3} }{2x} \\ \\ 2x \sqrt{2} = 16\sqrt{3} \\ \\ x \sqrt{2} = 8\sqrt{3} \\ \\ x = \dfrac{8 \sqrt{3} }{ \sqrt{2} } \\ \\ x = \dfrac{8 \sqrt{3} \times \sqrt{2} }{ \sqrt{2} \times \sqrt{2} } \\ \\ x = \dfrac{8 \sqrt{6} }{2} \\ \\ x = 4 \sqrt{6}$