According to Dell specs it has a SATA 2.5 inch hard drive.   I have a similar vintage 5577 model.  I have a full size SSD installed in the hard drive space, without any adapters and it is a "loose snug" fit. 5 years and no problems. Here is the link to service manual Inspiron 17 7737 Owner's Manual (dell.com)
Dear all,One of my remote clients has a dell notebook with the IDs from the picture bellow. Can you please tell me if the notebook uses standard S-ATA connections and we can add a standard S-ATA ssd without any adapter? Thank you!R [IMAGE]  
Dell Inspiron 7737 hdd/ssd S-ATA connections