Answer:
fourth option
Step-by-step explanation:
Using the sine and cosine ratios in the right triangle and exact values
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , cos60° = [tex]\frac{1}{2}[/tex] , then
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{4\sqrt{2} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2x = 4[tex]\sqrt{6}[/tex] ( divide both sides by 2 )
x = 2[tex]\sqrt{6}[/tex]
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cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{4\sqrt{2} }[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2y = 4[tex]\sqrt{2}[/tex] ( divide both sides by 2 )
y = 2[tex]\sqrt{2}[/tex]