Question

Plssss help
I need AC

Answer 1

∠ACB=90° ⇒ ΔABC is right triangle

AB is hypotenuse, ∠BAC=30° ⇒

`CB=(AB)/(2)=(12√(3) )/(2) =6√(3)`

Let's use Pythagorean theorem

`AB^2=BC^2+AC^2\\AC^2=AB^2-BC^2\\AC^2=(12√(3))^2-(6√(3) )^2\\AC=\sqrt{(12√(3)-6√(3))(12√(3)+6√(3)))} \\AC=\sqrt{6√(3)*18√(3) } \\AC=√(3*6*18) \\AC=18`

Answer 2

AC = 18

Explanation:

Using the cosine ratio in the right triangle and the exact value

cos30° =
`(√(3) )/(2)` , then

cos30° =
`(adjacent)/(hypotenuse)` =
`(AC)/(AB)` =
`(AC)/(12√(3) )` =
`(√(3) )/(2)` ( cross- multiply )

2 AC = 12
`√(3)` ×
`√(3)` = 12 × 3 = 36 ( divide both sides by 2 )

AC = 18