Question

In the right triangle shown, A = 30° and AC = 6.

How long is AB?
Answer exactly, using a radical if needed.

Answer 1

AB = 6√3

Explanation:

The triangle is a 30°, 60°, 90° triangle, and therefore side AC is equivalent to x√3, where x = length of the smallest side.

To find AB, we must first find x by dividing 6 by √3.

`(6)/(√(3)) = (6√(3))/(3)=3√(3)`

Therefore, x, in this case side BC, is equivalent to 3√3

Side AB, hour hypotenuse, is equal to 2x:

`2(3√(3))=6√(3)`

AB =
`6√(3)`