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Is there a way to find the angles of an isosceles triangle if you only know the length of the base? Here's an image:

isosceles triangle

If I know the length in red, is it possible to figure out what the angles in purple are?

Probably not, so in that case, let's then say I know the lengths of the black lines if the first is impossible.

Mortlanka
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    There are many isosceles triangles with the same base, hence the first question is trivial. The second question is trivial as well: if you know the side lengths of a triangle, you also know its angles by the cosine theorem. – Jack D'Aurizio Mar 27 '17 at 17:08
  • The isosceles triangle happens to be an extra-specially easy application of the cosine theorem, because the perpendicular bisector of the base divides the isosceles triangle into two congruent right triangles. – David K Mar 27 '17 at 17:26

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