Question

10 points! Please help if able!

Answer 1

The 30/60/90 right triangle is the biggest cliche in trig.  We recall the sides come in ratio $1:\sqrt{3}:2$

$1:\sqrt{3}:2 = x:y:4\sqrt{2}$

First x:

$\dfrac x 1 = \dfrac{4 \sqrt{2}}{2}$

$x = 2 \sqrt 2$

Next y:

$\dfrac{y}{\sqrt{3}} =\dfrac{x}{1}$

$y= 2 \sqrt{2} \sqrt{3} = 2 \sqrt{6}$

Choice C