The angle of elevation from the hiker to the park ranger is the same as the angle of depression from the ranger to the hiker, 29°.
The tangent function of an angle is the ratio of the opposite side (500') to the adjacent side (x) in the right triangle shown. That is tan(29°) = 500' / x
Multiplying the equation by x/tan(29°) gives x = 500' / tan(29°) x ≈ 500' / 0.5543 x ≈ 902 ft
Because of wind chill, they may say that the way it feels is -3, but it was probably much warmer, but later (at 12 degrees) they were probably reporting actually temp. This is my best guess.
