No, your equations are wrong.

First I thing you mean 34 not 43 but that is not the problem.

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tan 30=z/(1500+x)

tan 34=z/x

From the second equation we

x tan 34 =z

Thus,

x=z/(tan 34)

Substitute that into first equation,

tan 30=z/(1500+z/(tan 34))

This is a regular equation for z.

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Alterntiely you can dived your equations,

tan 30/tan 34=x/(1500+x)

Solve for x,

Then solve for z