Question

trigonometria: calcule x

Answer 1

Lei dos Senos 

a) $\frac{x}{sen60} = \frac{5 \sqrt{2} }{sen45}$
$\frac{x}{ \frac{ \sqrt{3} }{2} } = \frac{5 \sqrt{2} }{ \frac{ \sqrt{2} }{2} }$ Fazendo as devidas contas e racionalizando, dará:

$\frac{2 \sqrt{3}x }{3} = 10$
$2 \sqrt{3}x=30$
$\sqrt{3} x = 15$
$x = \frac{15}{ \sqrt{3} }$ (racionalizando e simplificando)
$x = 5 \sqrt{3}$

b)$\frac{x}{sen30} = \frac{8}{sen45}$
$\frac{x}{ \frac{1}{2} } = \frac{8}{ \frac{2}{ \sqrt{2} } }$
$2x= 8 \sqrt{2}$
$x=4 \sqrt{2}$