Here’s another way to look at it…
The quiz latitude is 77° 38′ 36.9″ S.
Cape Evans is at 77°38’S.
So what ever it is, it’s at the same latitude as Cape Evans. The latitude’s seconds specification is in the noise: 36.9″ = .62′ = .13 nautical miles, or just a short pub-crawl away. If I recall, the cross at Cape Evans is slightly south of the hut, so that could match — as could some of the dog skeletons.
Now let’s look at the longitude. The given longitude in the quiz is 166° 45′ 58.5″ E, right?
Cape Evans is at 166°24’E. Doing the math… ~46′ – 24′ = 22′, 22′ x .22nm/min = 4.84 nautical miles.)
So assuming your original quiz coordinates are correct, whatever it is lies roughly 5 nautical miles East of Cape Evans, basically on the western slope of Erebus.
The best online map of Erebus I can find is at:
Click on the “Big (250 KB)” link towards the bottom to get the map.
BTW, the location for Cape Evans comes from the New Zealand Antarctic Programme’s web site, http://www.antarcticanz.govt.nz/article/4003.html#5018