In the right triangle shown, A = 30° and AC = 6.
How long is AB?
Answer exactly, using a radical if needed.

AB = 6√3

Step-by-step 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.

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

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

AB =

2 x^2 -3x+p

sum of roots = 3/2

let other root be x

3+ x = 3/2

x= 3/2 - 3 = -3/2

product of roots = p/2

3× -3/2 = p/2

-9 = p

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