Question

I need some help with this

Answer 1

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