3D Trignometry problem - how to calculate the Horizontal distance?

Refer to the (very ordinary) 3d diagram below.

Formulae required to determine HD.

Slope Distance (SD), angles and dH are measureable.

A 3d soulition is required with no approximations, if possible.

Attachment 23693

Sorry one piece of information is missing; the azimuth of A'B' is also known.

It appears from your picture that ABB'A' is a parallelogram which means that AB and A'B' are the same length. Once you have that AB has length SD, which is given, and dH is given, it follows from the Pythagorean theorem that .

Unfortunately AB and A'B' are not the same length as the tilt angles at A and B are not equivalent.