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)=(opposite)/(hypotenuse)`

Substituting the values:

`cos(30)=(x)/(12√(3))`

Knowing cos(30) = √3/2:

`(√(3))/(2)=(x)/(12√(3))`

Multiplying both sides 12√3:

`\begin{gathered} (√(3))/(2)*12√(3)=(x)/(12√(3))*12√(3) \\ (12)/(2)*√(9)=x \\ 6*3=x \\ 18=x \end{gathered}`

Answer: D. 18.