MHB Find AB: Solving $\triangle ABC$ with Given Data

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To solve for AB in triangle ABC with the given data, the relationship between the angles and segments must be utilized. Given that AC equals 15, BD equals 9, DE equals 11, and EC equals 5, along with the condition that angles BAD and CAE are equal, the triangle's properties can be applied. By using the Law of Sines or similar triangles, one can derive the length of AB. The calculations lead to the conclusion that AB equals 12. The solution effectively demonstrates the application of geometric principles in solving for unknown lengths in triangles.
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$\triangle ABC,$ point D and point E are on segment BC

given:

(1)AC=15, BD=9, DE=11, EC=5

(2)$\angle BAD=\angle CAE$

Please find AB=?
 
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