The 30/60/90 right triangle is the biggest cliche in trig. We recall the sides come in ratio [tex]1:\sqrt{3}:2[/tex]
[tex]1:\sqrt{3}:2 = x:y:4\sqrt{2}[/tex]
First x:
[tex]\dfrac x 1 = \dfrac{4 \sqrt{2}}{2}[/tex]
[tex] x = 2 \sqrt 2[/tex]
Next y:
[tex]\dfrac{y}{\sqrt{3}} =\dfrac{x}{1}[/tex]
[tex]y= 2 \sqrt{2} \sqrt{3} = 2 \sqrt{6}[/tex]
Choice C
