I've been experimenting with this idea for a while now, because it's always confused me that there's no way to calculate stuff with trigonometry without either taking measurements in some way, or by using Pi to work out the value (which itself is calculated through measurements in some way).
I first worked on this a couple of years ago, but I gave up because I couldn't get past a certain problem I was having. But hopefully by posting here, maybe someone can figure it out better than me.
Let's consider that this rightangled triangle's sides are 3, 4 and 5. This standard triangle has been proven to have the angles 90, 36.9 and 53.1.
A = 36.9
B = 53.1
C = 90
a = 3
b = 4
c = 5
We can think of the angles as being in 'parts'. Assuming we want to calculate angle A, we know that A must make up a portion of 180  C (being the right angle). So A is part of 90.
The other part of the 90, is angle B. Now, to calculate one 'part', we do 90 / 7, where 7 is equal to the two affecting sides added together (a + b), (3 + 4). Because there are 7 parts in the 90, finding one part can be done by simply dividing by 7.
90 / 7 = 12.857
Now, to find out what A is, we just multiply by 3. This gives us 38.571. Of course, this doesn't equal 36.9. Try again with B, multiplying by 4. This gives us 51.428, which doesn't equal 53.1. You might notice though that the difference between the calculated value and the actual value is similar in both instances.
This is my problem:
When calculating an angle, the further away it is from 45 degrees, the bigger the difference. However, I can't seem to find a solid relationship between the two.
The formula that I have for this at the moment is:
Code:
A = a / 180  C \
\ a + b /
When trying this with the standard 1, 1, root 2, triangle (with angles 45 45 and 90), calculating either of the 45 angles using the formula works out with exactly 45. So I know that it's orienting around 45 in some way.
If anyone can figure out a solution to this, it would be appreciated greatly.
Thanks,
ShockWave.


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