If I have a solved triangle (i.e. three angles and three sides are known). And I know the coordinates of one point. What do I need more to know the coordinates of other points? And How to do it? Note that the triangle is Scalene (i.e. the sides and angles are not necessarily equals).
Solved triangle points
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geometry
trigonometry
triangles
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6No, the triangle can still pivot around that one known point. – 2017-01-16
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1And even if you "pin down" two vertices, the third one can flip across the line between the two specified vertices. – 2017-01-16
1 Answers
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If you have one known point in the triangle, the remaining coordinates are not determined because the triangle can still be at any rotation around that point.
If you have two known points on the triangle, the remaining coordinates are confined to two mirror-image positions of the triangle, but are not determined uniquely - unless you know the clockwise sequence of angles or side lengths, or the triangle is isosceles and the known points are on the axis of symmetry.
If you have three or more known points on the triangle which are in a straight line, the same problem as for two points arises - the mirror image problem is still present.
So in general you need coordinates for at least three known points that are not co-linear. The vertices would be an obvious choice, but other possibilities exist - there are a wide array of named points associated with triangles.