Trig w small angles 

[sin/tan divergence]
[easy to remember approximations]
The angle multiplyer.I've said a 2° degree thumb gives you a x30 distance. It's really more like 28.7 (1/sin(2°)). The error is consistently about 5% high, which seems well worth the simplification.
angle  multiplyer  error  (closer) 
1/4°  240  +5%  (229) 
0.5°  120  +5%  (114) 
1°  60  +5%  (57.3) 
2°  30  +5%  (28.6) 
6°  10  +5%  (9.57) 
10°  6  +4%  (5.76) 
20°  3  +3%  (2.92) 
Here is one simplification, admittedly not very simple.
We
should work out one with just 3 or 4 numbers to remember, as this
one's 5% error is excessively precise for most stuff.
angle  altitude factor sin(angle) 
ground distance cos(angle) 
0° (it's on the ground)  0  1 
10° (1 fist up)  1/6  1 
20° (2 fists up)  1/3  1 
30° (3 fists up)  1/2  5/6 
40° (4 fists up)  2/3  2/3 
50° (5 fists up)  2/3  2/3 
60° (3 fists down)  5/6  1/2 
70° (2 fists down)  1  1/3 
80° (1 fist down)  1  1/6 
90° (up)  1  0 
Comments encouraged.  Mitchell N Charity <mcharity@lcs.mit.edu> 