How to calculate slit separation?

[ipodmypod300]

Homework Statement

Light of wavelength 680 nm falls on two slits and produces an interference pattern in which the fourth order fringe is 38 mm from the central fringe on a screen 2.0 m away. What is the separation of the two slits?

Homework Equations

d * sin(theta) = m * lambda

The Attempt at a Solution

I tried to calculate the slit separation using the equation above but I'm not sure about the angle. Using tan^-1(.038/2), I got an angle of 1.1 degrees which then led me to a d value of 1.41 x 10^-4 m, but the answer given by the book is .085 mm so I'm just completely lost at this point.

 

[blue_leaf77]

I also get a similar answer as yours.

 

[ipodmypod300]

I also get a similar answer as yours.

Perhaps the book is wrong or something then.