MHB What Is $\angle ADB$ in a Plane with Given Side Lengths?

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The problem involves a geometric configuration with equal side lengths of 10 for segments AB, BC, CA, and CD, while segment AD measures 11. Participants discuss methods to determine the angle ADB using the given lengths. Various approaches, including the Law of Cosines and triangle properties, are explored to find the angle. The challenge lies in the non-standard triangle formed by the points. Ultimately, the goal is to calculate the precise measure of angle ADB based on the provided dimensions.
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In a plane we have :$\overline {AB}=\overline {BC}=\overline {CA}=\overline {CD}=10$ and $\overline {AD}=11$

find :$\angle ADB=?$
 
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johng said:
Simple solution:
very nice!
 

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