Half-Life is Vert- by default, that is the game doesn't dynamically increase your field of view (FOV) when you choose a wide aspect ratio, it just cuts off the top and bottom parts of the camera view port.

Right-click on the game in your Steam library, choose Properties, then Set launch options..., type +default_fov 106.

106 is good for 16:9, but you can use any value you want. The default value is 90 for 4:3, you can use an online FOV calculator to calculate the new value for your aspect ratio. I recommend 100 for 16:10 and 122 for 21:9.