Answer:
2nd option
Step-by-step explanation:
using the cosine and sine ratios in the right triangle and the exact values
cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] and sin30° = [tex]\frac{1}{2}[/tex] , then
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{12\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2x = 12[tex]\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex] = 36 ( divide both sides by 2 )
x = 18
and
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{12\sqrt{3} }[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2y = 12[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
y = 6[tex]\sqrt{3}[/tex]
