Answer:
B
Step-by-step explanation:
First calculate BD using sine ratio in Δ BCD and the exact value
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex], thus
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BD}{BC}[/tex] = [tex]\frac{BD}{12}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2BD = 12[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
BD = 6[tex]\sqrt{3}[/tex]
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Calculate AD using the tangent ratio in Δ ABD and the exact value
tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , thus
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AD}{BD}[/tex] = [tex]\frac{AD}{6\sqrt{3} }[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
[tex]\sqrt{3}[/tex] AD = 6[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
AD = 6 → B
