Appropriate cable?

Does the TV and PC both support VGA connection? If so then yes, but only if you don't have a digital connection to choose otherwise. If you have a DVI, HDMI, or Display Port to use instead, those would be preferable over analog signaling.
 
Remember that going with the connection you showed us in the pic will NOT transfer sound. It will also give you a lower quality video signal.
 
If that is the only output option you are not going to have any choice. If the TV has that input it also has a 3.5mm headphone jack (or LR RCA) for audio in. As long as you aren't exceeding 1366x768 the quality loss will be negligible, especially if you are using that cable and not a longer one.

Now if the PC also has other video out options (some will have that and a small digital), then sure, you should use the digital. Depending on the card you can have (generally) up to 3 output options. Its not worth speculating further without knowing more information.
 
Back