How do i solve this triangle question

http://www.box.net/shared/upahshj9rqnkp68hlcvp

in this triangle,

if it is given that the side AD is 6, how do i figure out the length of BC?

This is a law of sines problem. We need to figure out x

Triangle DBC is an isosceles triangle, so angle DBC = 180 - 2x - 2x = 180 - 4x

Angle ABC = 180 - x - 2x = 180 - 3x

Angle ABD = ABC - DBC = 180 - 3x - (180 - 4x) = x

AD = 6

From the Law of Sines

sin(ABD) / AD = sin(x) / BD

sin(x) / AD = sin(x) / BD

1/AD = 1/BD

BD = AD ==> BD = 6

Since DBC is an isosceles triangle, BD = BC = 6

.got it openend now. if.you use the pythagorean theorem, then 2x .squared +2xsquared =bc solve 16xsquared =bcsquared, take square root of both sides, bc=4 . ad has nothing to do with this,

Angle ADB = 180-2x
Therefore Angle ABD = x
Therefore AD = BD = 6
Triangle BDC is isosceles
BD = BC = 6
Answer BC = 6