The given scenario is illustrated in the diagram shown below
The given triangle is a right triangle
BC represents the height of the tree
AD represents the number of feet that he walked backward.
Considering triangle BCD with angle D as the reference angle,
opposite side = BC = 80
adjacent side = BD
We would find BD by applying the tangent trigonometric ratio which is expressed as
Tanθ = opposite side/adjacent side
Thus,
Tan68 = 80/BD
By crossmultiplying, we have
80 = BDTan68
BD = 80/Tan68 = 32.32
Considering triangle ABC with angle A as the reference angle,
adjacent side = AB = AD + 32.32
opposite side = 80
Thus,
Tan 41 = 80/(AD + 32.32)
By crossmultiplying, we have
(AD + 32.32) Tan41 = 80
(AD + 32.32) = 80/tan41 = 92.03
AD = 92.03 - 32.32
AD = 59.71
Corey stepped back 59.71 feet