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perhaps the Q meant this
|dw:1350751784378:dw|

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yeah this is related rate.

|dw:1350751925717:dw|

If i interpreted the problem correctly ...

How did you get z=16.14?

forget that ... it's not necessary.

Given area is constant ... dA/dt = 0

Would I differentiate A=.5 xysin(theta) ? What would I take the derivative with respect to?

time ... t,
also you are given the values of dx/dt and dy/dt

dA/dt=.5 (dx/dt)ysin(theta)+x(dy/dt)sin(theta)+xy(theta)(cos(theta))(dtheta/dt) ?

Got it! Thanks!