Question

In the right triangle shown, ZA = 30° and AB = 4V3.

Answer 1

The length of AC is 8

Explanation:

Given that ABC is a right angled triangle.

The measure of angle A is $\angle A=30^{\circ}$ and $AB=4\sqrt{3}$

Length of AC:

Using the trigonometric ratios, we have,

$cos \ 30^{\circ}=\frac{adj}{hyp}$

where $adj = 4\sqrt{3}$ and $hyp=AC$

Substituting the values, we have,

$\frac{\sqrt{3}}{2}} =\frac{4\sqrt{3}}{AC}$

Multiplying both sides of the equation by AC, we get,

$AC\frac{\sqrt{3}}{2}} ={4\sqrt{3}$

Multiplying both sides by $\frac{2}{\sqrt{3} }$, we get,

$AC={4\sqrt{3}\times (\frac{2}{\sqrt{3} } )$

Simplifying, we get,

$AC=8$

Thus, the length of AC is 8