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