Law of Sines, Sin(A)/a = sin(B)/b =sin(C)/c, where A, B and C are the angles of the right triangle formed when a, b and c are the distances between angles. For this to work, you need to know the height of the target from the ground up (label this as a) as well as two angles: one is given, the 90deg. at the base of the target (call it B) and the other angle C atop the target can be derived (180-90-A = C) once the angle A is measured from the shooting position using a protractor of sorts or another device (the triangle measured can also be inverted so as to measure distance from the top of the target as opposed to the firing position; this may give more room to make measurements). But using plain degress will only get you so far with distance and accuracy.
To get good accurate data for long distance, we need to use something finer than degrees. Use MOA in these equations, so sin(A/60)/a, so on and so forth, should do it. So basically you want to measure 60 units within one degree. To measure, you'll either need the worlds largest protractor, an expensive surveying kit --or a cheap home made MOA protractor.
Fix a protractor to either the top or bottom left of a large, strudy and warp free piece of plywood. Fix it semicircle side down if up top and inverting the triangle, or semicircle side up if on the bottom and measuring from the ground in the shooting position. Attach it a few inches from the edges. If fixing it up top, attach the plywood to a fence stake so you can level the device and get it the same height as the top of the target. Now attach string to the center of the protractor and measure out on the far edge of the plywood an arc 1 deg. in length. Then bisect this over and over until you have 60 units. Attach a yardstick or similar long, straight and flat smooth stick, sighted along the string, and use this to aim down and find the mark on the protractor. You now have an MOA protractor suitable for measuring accurately to long distances given only the target height and the angle the target sets to the ground. Cool, huh?
Say the target is 5' and you measure using the rig that the target is 1/10th of one degree. And law of sines gives sin(10/60)/5 = sin(89+50/60)/c. We want c as it is the length to the target (we really aren't concerned with B and b here). So just fill in the formula using only sin(A)/a = sin(C)/c, convert to a/sin(A) = c/sin(C) and then cross multiply to isolate c and you get: c= 5sin(89+5/6)/sin(1/6) = 1718.87', or 572.96 yards.
If the target were 5 MOA away, it would be 5sin(85+55/60)/sin(5/60) = 3437.74', or 1145.91 yards.
The farthest you can measure without going to fraction of MOA is 5729.58 yards using a 5' target.
This method can be extremely accurate, it depends on how precise you set it up. It is ideal for setting up precise distances for targets, or finding precise distances period, once you have an accurate measure of an item at target distance. It would be a good long range tool for precise target distances, but obviously this isn't something you carry around with you all the time. Anyway, I thought I'd throw it out there.