Question

In the right triangle shown, mZA = 30° andAB= 12√3.B12√3How long is AC?Choose 1 answer:6O 6√3121824

Answer 1

ABC is a right triangle, and the measures are:

hypotenuse = AB = 12√3

angle = 30°

adjacent side to 30 ° = x

Knowing that, use the formula of cosine to find x.

The formula of cos is:

$cos(A)=\frac{opposite}{hypotenuse}$

Substituting the values:

$cos(30)=\frac{x}{12\sqrt{3}}$

Knowing cos(30) = √3/2:

$\frac{\sqrt{3}}{2}=\frac{x}{12\sqrt{3}}$

Multiplying both sides 12√3:

$\begin{gathered} \frac{\sqrt{3}}{2}*12\sqrt{3}=\frac{x}{12\sqrt{3}}*12\sqrt{3} \\ \frac{12}{2}*\sqrt{9}=x \\ 6*3=x \\ 18=x \end{gathered}$

Answer: D. 18.