Question i need a cpu cooler for lga 1150

Please list the specs to your build like so:
Motherboard:
Ram:
SSD/HDD:
GPU:
PSU:
Chassis:

Also, what sort of a budget have you allocated for the cooler purchase? Your(or your friend's) location? Your preferred site or purchase?


Motherboard: Z87-G41 PC Mate
Ram: 4 sticks of 4GB ddr3 1333
SSD/HDD: 2TB hybrid SSHD
GPU: MSI GTX 1050 Ti GAMING X
PSU: Thermaltake Smart 500W 80+ White Certified PSU
Chassis: no idea who makes it got it for 10$ used im gonna assume generic early to mid 2000's case

amazon newegg or ebay is where i prefer to purchase. the cooler must be under 145mm in height due to the limitations of my friends case budget 40$ or less located in tucson az usa
 
so im building a socket 1150 computer for a friend using a 4790 non k the only issue is the only case i have on hand cant take a cooler higher than 6 inches as thats the measurement i took when i measured from the top of the cpu ihs to the edge of the case where the side panel would go

this is the cooler im currently looking at https://www.thermalright.com/product/assassin-x-90-se/
I have an old computer I keep around for emergencies. It has an Asus H97i motherboard with a 4790S cpu and its mounted in a Silverstone Grandia 09 case. I use the Noctua NH-C14S cooler for that. It has a low profile and depending on how much room you have in your case you can use either 1 fan below the radiator or 2 fans 1 above and 1 below. My case only fits 1 below but since its a 140mm fan blowing down it cools well.
 
I have an old computer I keep around for emergencies. It has an Asus H97i motherboard with a 4790S cpu and its mounted in a Silverstone Grandia 09 case. I use the Noctua NH-C14S cooler for that. It has a low profile and depending on how much room you have in your case you can use either 1 fan below the radiator or 2 fans 1 above and 1 below. My case only fits 1 below but since its a 140mm fan blowing down it cools well.
that cooler is way outta the budget i only got 40$ to spend on a cooler
 
so im building a socket 1150 computer for a friend using a 4790 non k the only issue is the only case i have on hand cant take a cooler higher than 6 inches as thats the measurement i took when i measured from the top of the cpu ihs to the edge of the case where the side panel would go

this is the cooler im currently looking at https://www.thermalright.com/product/assassin-x-90-se/

what is the case called ?

that cooler would be fine as its around 12.5cm

this would be fine for a non k unit also