The length of AC is 8
Explanation:
Given that ABC is a right angled triangle.
The measure of angle A is [tex]\angle A=30^{\circ}[/tex] and [tex]AB=4\sqrt{3}[/tex]
Length of AC:
Using the trigonometric ratios, we have,
[tex]cos \ 30^{\circ}=\frac{adj}{hyp}[/tex]
where [tex]adj = 4\sqrt{3}[/tex] and [tex]hyp=AC[/tex]
Substituting the values, we have,
[tex]\frac{\sqrt{3}}{2}} =\frac{4\sqrt{3}}{AC}[/tex]
Multiplying both sides of the equation by AC, we get,
[tex]AC\frac{\sqrt{3}}{2}} ={4\sqrt{3}[/tex]
Multiplying both sides by [tex]\frac{2}{\sqrt{3} }[/tex], we get,
[tex]AC={4\sqrt{3}\times (\frac{2}{\sqrt{3} } )[/tex]
Simplifying, we get,
[tex]AC=8[/tex]
Thus, the length of AC is 8
