Out West where I grew up, cougars share the landscape with us and since the 70's ,cougar attacks are on the rise, some fatal.
Cougars are a concern even now, as the animals sometimes wander down to the edges of the subdivisions that border the hills.
If you do run across a cougar in the wild, here are some safety tips.
Never approach a cougar. Most likely they'd prefer to avoid a confrontation, but like all wild animals, they can be unprectible. A cougar feeding on a kill is very dangerous.
Always give a cougar an avenue of escape.
Stay calm. Talk to the cougar in a confident voice. If you have a small child with you, pick them up off the ground and have older kids slowly back up towards you. Children frighten easily and their rapid movement could provoke an attack.
Do not run (remember that whole sudden movement thing). Try to back away from the cougar slowly. Sudden flight may trigger an instinctive attack.
Watch for signs, if you see signs of a cougar, young, spoor, scat, a kill area, leave the area immediately. Some signs are obvious, but as the cougars enter the fringes of urban areas, the signs may be harder to spot.