Find intersection of data on a chart.

Looks like it should be a simple 2D lookup using the approximate match option in the MATCH() function (3rd argument is 1). Unfortunately, almost all of the lookup examples on the internet are all exact match examples, so one has to be aware of the approximate match option and try a few on their own to figure out how it works. Here's what I would do:

0) If you are unfamiliar with Excel's INDEX() and MATCH() functions, review the help files and any other tutorials you are familiar with:
https://support.office.com/en-us/art...2-b56b061328bd
https://support.office.com/en-us/art...9-533f4a37673a
1a) Assuming you are allowed to edit the lookup table, enter the lower limits for the dry bulb temparatures. A2 is 10, A3 is 30, A4 is 50, etc.
1b) Enter the lower limits in the relative humidity row. B1 is 0, C1 is 5, D1 is 10, and so on.
2) Use a MATCH() function to return the row number =MATCH(dry_bulb_temp,$A$2:$A$7,1)
3) use another MATCH() function to return the column number =MATCH(relative_humidity,$B$1:$V$1,1)
4) Use an INDEX() function to return the final result =INDEX($B$2:$V$7,result of 2,result of 1) or, if you feel a desperate need to nest those functions into one =INDEX($B$2:$V$7,MATCH(dry_bulb_temp,...),MATCH(relative_humidity,...).

Will that work for you?