ABC is a triangle. Points D and E lie on sides AC and BC, respectively.Given angle BAC=30 degrees, angle ACB=15 degrees, AB=BD and DE=EC, what is AD:CD?

Answer 1

Answer 2

Since triangle ABD is isosceles with vertex angle 120 degrees, AD=AB√3

Triangle BDC is also isosceles (base angles equal); therefore BD=AB=CD.

That gives you the required ratio.