It's important to understand that we "share" the country with many types of wild animals. Personally, I fear wild dogs more than most other species, just because a pack of wild dogs tend to have less fear of humans than other species (except, of course, other humans).
When you see tracks of predatory animals you are in their territory. You may want to explore other venues in the future because you may be at greater risk on that trail.
Prevention is pretty important to personal protection. Scent and noise are valuable deterrents.
The Scandinavians have believed for centuries that bells help prevent wildlife encounters and I believe that too. A pair of bells on a lanyard around your neck is a simple and good strategy. Talking in a loud voice, even just talking to yourself, is another tactic, as is singing.
For scent-based protection I have tested 3 which work for small wildlife, and which may work as a deterrent for large wildlife as well; no guarantees. Peppermint oil extract, fresh-ground black pepper and ammonia.
Years ago, I was active with my son in the Boy Scouts. One of the places we went to every year was Camp Lowden, a Boy Scout campground. It had a terrible problem with raccoons, and, at the time, we used an old GI issue canvas lean-to tent for provisions. Every night the 'coons would sneak into the tent and get into the provisions. That quickly got old so I grabbed my pepper mill from my own provisions and put a healthy dose around the tent as a scent barrier. While I peppered the tent every morning and every evening afterward, the raccoons stayed away. I also found out that racoons have the cutest sneeze.
I've used peppermint oil for both mice and squirrel problems. For a residence without family pets, peppermint oil is a good deterrent, and more effective overall than traps or poisons. Peppermint oil is also supposed to be good to help hide food scents on your person, so that may help in some wild animal encounters.
I've used ammonia now on 2 occasions against outdoor squirrels. In the first case, a squirrel living in a tree near my back door had become aggressive, and it rushed me on a couple of occasions. I used a carpet cleaner, I think it was designed for pet cleanup, and it had a pretty strong ammonia scent. I sprayed the side of the tree closest to the house while the squirrel watched. The squirrel got pretty upset that I had so potently peed the tree, but it left me alone afterward. Later, it must have moved out of the tree, because the nest appeared to be picked apart by birds.
More recently some squirrels were hiding inside my car, probably in the engine compartment. I purchased some ammonia all-purpose cleaner and sprinkled that around 3-sides of the car. (Always leave an avenue for the animals to leave in.) Watching to see if a reapplication is required.
Finally, "Bear Spray" is a known deterrent for cougars/mountain lions actively stalking humans, demonstrated here: