Answer:
x = 8, y = 4
Step-by-step explanation:
To find x use the sine ratio in the right triangle and the exact value
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , thus
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{4\sqrt{3} }{x}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
x × [tex]\sqrt{3}[/tex] = 8[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
x = 8
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To find y use the tangent ratio in the right triangle and the exact value
tan60° = [tex]\sqrt{3}[/tex] , thus
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{4\sqrt{3} }{y}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by y )
4[tex]\sqrt{3}[/tex] = y × [tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
y = 4
