If the 770 uses the reference cooler it is safe to assume it is the size listed on the Geforce site. However, it's always good to double check and any manufacture proprietary cooler or card would or could be longer or wider.
I lean toward MSI or ASUS cards. I've had good experiences with ASUS customer support. MSI and ASUS also have very good coolers if you go for a non stock cooler.
This MSI says it's 10.24"http://www.newegg.com/Product/Product.aspx?Item=N82E16814127741