Question 960990

I posted before. Could I get steps on how to solve this. If possible algebraically, I have to know how to solve it without a calculator.

Solve for x (x=AB) in the figure shown
CD=200 

http://i.imgur.com/PqcA5E3.png 
<pre>From &#8710;BDC, tan &#8736DBC = {{{O/A}}}
{{{tan 60^o = DC/BD}}}
{{{tan 60^o = 200/BD}}}
{{{BD * tan 60^o = 200}}} ------- Cross-multiplying
{{{BD = 200/tan 60^o}}}
{{{BD = 200}}}{{{"÷"}}}{{{(sin 60^o/cos 60^o)}}} ------ {{{tan 60^o = (sin 60^o)/(cos 60^o)}}}
{{{BD = 200}}}{{{"÷"}}}{{{(sqrt(3)/2)/(1/2)}}} ------ {{{sin 60^o = sqrt(3)/2}}} and {{{cos 60^o = 1/2}}}
{{{BD = 200}}}{{{"÷"}}}({{{sqrt(3)/2}}}{{{"÷"}}}{{{1/2}}})
{{{BD = 200}}}{{{"÷"}}}({{{sqrt(3)/2}}}{{{"*"}}}{{{2/1}}})
{{{BD = 200/sqrt(3)}}}, or {{{200sqrt(3)/3}}}

From &#8710;ABD, sin &#8736BAD = {{{O/H}}}
{{{sin 60^o = BD/AB}}}
{{{sin 60^o = BD/x}}} 
{{{sin 60^o = (200sqrt(3)/3)/x}}}
{{{x * sin 60^o = (200sqrt(3))/3}}} --------- Cross-multiplying
{{{x = 200sqrt(3)/3}}}{{{"÷"}}}{{{sin 60^o}}}
{{{x = 200sqrt(3)/3}}}{{{"÷"}}}{{{sqrt(3)/2}}}
{{{x = 200sqrt(3)/3}}}{{{"*"}}}{{{2/sqrt(3)}}}
{{{x = 200cross(sqrt(3))/3}}}{{{"*"}}}{{{2/cross(sqrt(3))}}}
AB, or {{{highlight_green(x = 400/3)}}}