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Quick single slit diffraction question

In a single-slit diffraction pattern, the central fringe is 430 times as wide as than the slit. The screen is 17500 times farther from the slit than the slit is wide. What is the ratio /W, where is the wavelength of the light shining through the slit and W is the width of the slit? Assume that the angle that locates a dark fringe on the screen is small, so that sin tan .
wrong check mark




2. sin theta = m x lamba/w
tan theta = sin theta




3.since the central fringe is 430w and the length is 17500w, i figured the ratio would be 430w/17500w = 430/17500 = lamba/w. This is not correct.

Any thoughts?
 

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