So the first part of doing it only using Spatial tools was straight forward fun
The other part - not so much, but I gave it a go - after all, how hard could it be?
Especially since I have just helped the daughter with some high school trigonometry - now I am afraid she won't pass her grades with her fathers assistance 😂
On my way to Lhotse Face
Not sure why non-special (trig) is giving a slightly different answer. Used ACOS instead of ASIN and my distances matched the solution when I checked them (check not in final solution). When I ran the posted solution using ACOS it matched my answer. Trigonometry should give the same result for ASIN (length Opposite/length Hypotenuse) as ACOS (length Adjacent)/length Hypotenuse). Let me know if someone knows differently.