# Trigonometric Lengths

Geometry Level 3

In triangle $$ABC$$, $$\angle ACB = 90^\circ$$. $$A, D, E,$$ and $$B$$ are consecutive points on $$AB$$ such that $$\overline{AD}=\overline{DE}=\overline{EB}$$. If there exists $$\theta$$ such that $$\overline{CD} = 5 \cos \theta$$ and $$\overline{CE} = 5 \sin \theta$$, what is $$\overline{AB}^2?$$

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