3 ms·
If you used the difference in height over the actual distance traveled instead of the horizontal distance, then 100 % would indeed be vertical. I.e. instead of
by danbruc 9y ago
If you used the difference in height over the actual distance traveled instead of the horizontal distance, then 100 % would indeed be vertical. I.e. instead of using sin(a)/cos(a) you could just use sin(a) and for small angles the values are close but the later one approaches 1 while the former one diverges as you approach 90°. I would probably have picked the later one but the former one is probably somewhat easier to work with in practice, e.g. for construction work.
- Sharlin 9y ago> sin(a)/cos(a) Also called tan(a) ;)
- danbruc 9y agoThe other variant was actually meant to read sin(a)/1 to highlight the ratio in both cases but I abandoned that halfway through because I thought it makes the hypotenuse look special while it really is not in the sin(a)/cos(a) variant where the more natural description would be tan(a)/1 but that kind of ruins the simple association with the side lengths of a right triangle. I had another idea how to formulate it that would not favor one of the variants but as far as I can tell the necessary distinction between the two catheti that exists in German does not exist in English and so I left it as it is.