Actually, you don't need right angles. What you need to know is that the side of any triangle divided by the sine of the angle opposite that side is equal to any other side of the same triangle divided by the sine of it's opposite angle (the reciprocal is also valid). The law of sines is thus:

sin a/A=sin b/B=sin c/C where the lower case a, b, and c are all sides of the same triangle, and the upper case A, B, and C are all three angles of the same triangle respectively. If you know a landmark and can get a decent bearing on it relative to north, then you can move in a direction for a given distance (paces) and shoot another bearing and if the two points are relatively far enough apart to generate a significant angular difference, you can then figure out how far you are from the landmark and in which direction. If you know where you want to be (ie base camp) and it's relative location to the landmark, you now have a bearing and rough distance to get there.

Essentially, all you need is two sides and one angle of the triangle, or one side and two angles. You don't need a map except at the very beginning to determine base camp relative to the lanmark. You can also do this if you have two landmarks and no other reference point (including a memorized map location).

Trigonometry is pretty cool. Even if I hadn't been an electronics tech, I would still have found a use for that once boring class.

Here's an excellent link that demonstrates how to use the law of sines, including the deductive arithmetic that starts to make it work with just a compass.

http://www.wisc-online.com/objects/index_tj.asp?objid=TMH2702

If you need more help or haven't gone through a trig class (I highly recommend it), you should contact a math professor and see if you can get in on a class.