You should have no problems fitting this card into the case.
PCPartPicker part list: https://pcpartpicker.com/list/ztmsxY
Price breakdown by merchant: https://pcpartpicker.com/list/ztmsxY/by_merchant/
Motherboard: ASRock H110M-ITX/ac Mini ITX LGA1151 Motherboard ($69.99 @ SuperBiiz)
Video Card: MSI GeForce GTX 1050 Ti 4GB Video Card ($139.99 @ B&H)
Case: Thermaltake Core V1 Mini ITX Tower Case ($42.99 @ SuperBiiz)
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-03-21 07:31 EDT-0400