Would appreciate any help on the following problem, Thank You!
given $\displaystyle AB = 2$
BC is the hypotenuse of the 45-45-90 triangle ...
$\displaystyle BC = (AB)\sqrt{2} = 2\sqrt{2}$
BC is also the longer leg of a 30-60-90 triangle ... BC is the short leg.
$\displaystyle BD = \frac{2\sqrt{2}}{\sqrt{3}} = \frac{2\sqrt{6}}{3}$
from this point, you should be able to finish up.