I believe the broken part is a Pivot Locking Shoe with the following measurements, W-1 1/4", D-1/2", L-2".
What parts do I need to order and any other helpful information would be appreciated.
![IMG_20210719_122520835_HDR](images/pictures/2024/01/735681.jpg)
![IMG_20210719_122635272_HDR](images/pictures/2024/01/735680.jpg)
The pivot shoe you have appears to be the 15-129 Pivot Shoe. To confirm that this is the right replacement, you'll need to remove the shoe from the window and carefully double check the dimensions. Although, I am confident this is the shoe you'll need.
Your channel balance attachment is the terminal clip used on the Series 770 Channel Balance. Since yours has a 2900 stamp, I believe you'll need the S770-29 which has a 29" channel length.
Unfortunately, I am unable to cross-reference the stamp you have, so you'll need to obtain the exact weight of the sash. There is a chart below the product description of the balances that details the weight ranges each stamp option can support.
I am not sure if you'll need to replace the compatible pivot bar, however, I'll need to see it removed from the bottom of the sash to identify the right replacement.