If two observers are watching a climber on the opposite face of the chasm. The chasm is 81 feet wide. When observer A looks down to the bott

Melody, this is how I pictured it:

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I'm going to assume that observer B is at the bottom of the chasm, on the same side as observer A.

In this case:

The height of the chasm is given by 81*tan(51°)

The height of the climber is given by 81*tan(θ)  where θ is the as yet unknown angle of elevation of the climber as seen by observer B.

The distance of the climber below the top of the chasm is given by 81*tan(20°).

Since the last two added together must equal the height of the chasm we have:

 81*tan(θ) + 81*tan(20°) = 81*tan(51°)

tan(θ) + tan(20°) = tan(51°)

tan(θ)  = tan(51°) - tan(20°)

θ = tan^-1(tan(51°) - tan(20°))

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left(\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{51}}^\circ\right)}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{20}}^\circ\right)}\right)} = {\mathtt{41.053\: \!483\: \!814\: \!122^{\circ}}}$$

so θ ≈ 41°

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It is all  too much for me Alan, the question makes no sense (not to me anyway)

Thanks Alan  :)