Finding an angle with limited info :)

[barrett777]

I am looking for a point of intersection between two lines, but I can figure out the rest if you can help me find an angle. I will have many scenarios that fit the criteria below, this isn't just one triangle, so please help me find an equation that can be used for the criteria below. I'm kind of rusty so (hopefully) this may be a simple answer.

This triangle can be acute or obtuse, but not oblique. This is a 'normal' triangle with angles A, B, C, and sides a, b, c (across from their respective angle).

I know the length of side c.

I know angles A and B, and they are equal to each other.

I don't know the length of side a or b, but I know that they are equal to each other as well.

I need to find the missing information. How can I use this information to find the length of the equal sides a and b, and find angle C?

Thanks for your help,
Ben

[aerobert]

So, you have an isosceles triangle - you told us A=B, so also a=b

You can bisect the other angle (C) to bisect the other side (c), thus you have a right triangle (c/2)/a=sin(C/2)

Robert

[barrett777]

Okay I'm farther along now, one last step and hopefully this is okay. This question is actually a programming question, and so in my example all three points of the triangle are on a 2D graph, and what I actually need is (x, y) coordinates for the third point.

I now know all three side lengths, and all three angles.

I also know the (x, y) coordinates for points A and B.

How can I use this information to find the (x, y) coordinates for point C?

Thanks for your help