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Old 26-07-2008, 10:12 PM   #1
_r.u.s.s.
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you said
Quote:
The segments BC = CD but have no known value.

Angle ACB + ACD = 180 degrees (due to the fact that the 4th line is a straight line).
that makes ACD 90 degrees

oops edit: actually i thought you mean something else with second line, nevermind
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Old 26-07-2008, 10:13 PM   #2
Mighty Midget
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No, one could be 30 and the other 150 degrees. As for BC = CD, that doesn't guaranty a right angle either
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Old 27-07-2008, 12:23 PM   #3
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Quote:
Originally Posted by Mighty Midget View Post
Can one calculate, based on the angles BAC and CAD, the angles ABC, ACB, ACD or ADC?
I would say no, but don't pin me down.
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Old 27-07-2008, 12:33 PM   #4
Mighty Midget
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That might very well be possible, seeing the lack of data for this particular psoblem. The interesting bit is to see how any difference between the two known angles influence the direction of the 4th line.
If they are both equal and do not equal to zero, then the 4th line is perpendicular to line c.

If they are both equal and equal to zero, then the 4th line is at 0 or 180 degrees on the c line.

If the angle BAC is greater than CAD, then the 4th line is at an angle "a" on the c line 90 < a < 180

If the angle BAC is smaller than CAD, then the 4th line is at an angle at the c line at 0 < a < 90

So, there is some sort of relationship here. The question is is it predictable and can it be calculated?
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Old 27-07-2008, 12:55 PM   #5
_r.u.s.s.
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what you want to know are the angles only, right? and if you drag the E line further or closer it doesn't matter for angles, they stay the same, as long as BC=CD of course.

so you can pick any value for BC or CD. then it could be calculated
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Old 27-07-2008, 01:06 PM   #6
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But e has no determined direction.
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Old 27-07-2008, 01:18 PM   #7
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For starter this is how I look @ trigonometry:



Therefor your problem will look like the following in my opinion:



Now you end up wit 3 triangles.. (yes 3)

Namely: ABC ; ACD & ABD

To solve your issue I NEED (besides the known 3 angles @ A)
Either 2 sides OR 1 additional angle AND 1 side.

Or else there can't be a solution.
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Old 27-07-2008, 01:09 PM   #8
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Perhaps _r.u.s.s. is onto something. Like he says, the lengths AB, AC or AD doesn't change the angles I'm after, but once you fix one length, the others are set, even though they are still unknown.
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Old 27-07-2008, 01:13 PM   #9
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luchsen it has, because there is only one possible way to place the line so the BC and DC are equal
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