Optics: light refraction in prisms

[alingy1]

Could you please check the following problem?
The book made an approximation. I didn't in my method. But the difference seems considerable. Did I make a mistake?

 

[TSny]

Your analysis looks good. I think maybe the textbook was assuming a different relative orientation between the prism and the wall. See attached figure. But the problem statement is not clear on this point.

 

[alingy1]

EDIT: I get it now.
But, would using that approximation be fine for my picture?