how to find the third vertex

Quote:

Originally Posted by ragsk

Known two vertices A(x1,y1) and B(x2,y2) of a triangle, how to find the third vertex C(x3,y3)? Also known the length of AB as a units and angle B = alpha degrees.

Well i wud like to know the general method(which include only variables) to find the third vertex, So that i can get the result just by applying the formula.

The only unknowns angle A,angle C,length of BC and length of CA.

I tried to figure it out assuming that a cirlce that passes thru these three vertices as shown in the attachment..............

But i cud'nt succeed. Please help me.

You will not succeed, because the constraints are not enough to pin the vertex C in one fixed place.
Per the givens, point C is free to be anywhere on that ray (BC) of the known angle B---as long as point C does not coincide with point B.

If C is close to B, angle A will be small. As C goes away from B, the angle A becomes bigger. There are infinitely many answers as per the givens.

If the circle that you thought of has a known dimension---radius, diameter, circumference, coordinates of the center,....---then there will be only one answer. If the circle has no known dimension, then there are infinitely many answers.