… the actual solution from the text is 204.26 …

Their solution is off by a centimeter, due to rounding intermediate results (known as 'round-off error').

… it says to round … lengths to two decimal places …

That instruction pertains to final answers only. Were we to round

*intermediate* lengths to two places, the round-off error would increase.

Your answer is off by 2 cm because of round-off error. You can avoid that, by rounding every intermediate value to five places instead of four.

I would have expected that rounding intermediate results to four places would have been sufficient (it was, using my approach to estimate b), but you calculated b via two additional sine values, and the rounding of those sines is what changed your final answer a tiny bit. Alternatively, you could round the lengths to four places and

*not* round any trigonometric values displayed by the calculator (that is, let the calculator carry all digits for subsequent calculations, by using its memory features).

Assuming that round-off error has not been covered in your class, your work is good. I would have given you full credit.