You want a WiFi router with what's called client or client/bridge mode (not to be confused with plain bridge mode which often means it can only connect to another identical WiFi router). There are several routers on the market which can do it. But the cheapest route is to find a used one that's compatible with DD-WRT. After you get DD-WRT installed on it, it supports client/bridge mode.
http://www.dd-wrt.com/wiki/index.php/Client_Bridged
Be forewarned that DD-WRT's implementation is a bit buggy in that the bridge won't connect immediately after you associate with the desired SSID. You have to reboot the router first before it will connect.
And Client mode means the router connects to the WiFi network as if it were plugged into the WAN port. The router adds a firewall and does NAT, effectively shielding devices you plug into the router's LAN ports from being accessed via the WiFi network. In client/bridge mode, the router acts like a big WiFi adapter for every device plugged into its LAN ports. These devices get an IP address from the main router (the one producing the WiFi network you're connecting to), and can be seen by devices connected to the main network.
Since your computer has both WiFi and ethernet, if you're willing to leave it on all the time it's possible to do it without a router. It was fairly straightforward in Windows 7, but Microsoft has made it a lot more difficult to use with Windows 10. (You may have to swap the network cards in these instructions, as most people doing this want to take an ethernet connection and turn their laptop into a WiFi hotspot - the opposite of what you want to do.)
http://www.dummies.com/computers/operating-systems/windows-7/how-to-share-an-internet-connection-in-windows-7/
http://www.informit.com/articles/article.aspx?p=2455390&seqNum=6
But a computer left on 24/7 for a few years will use as much extra electricity as a cheap WiFi router will cost you, so I'd recommend going the WiFi router + DD-WRT route.
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