Square Lounge Drunken Shopper

After a long dinner, a man named Edward is lying inside a lounge in the shape of square ABCD, in such a position that triangle DEC is equilateral. A second person, Frank, is lying on edge BC with |EB| = |EF|. What is the size of angle CEF?

Final Answer:

x =  45 °

Step-by-step explanation:

$$\begin{gathered} a=1 \\ h=\sqrt{3}/2\cdot a=\sqrt{3}/2\cdot 1\doteq 0.866 \\ b=a-h=1-0.866\doteq 0.134 \\ \tan y=b:a/2 \\ y=\frac{180°}{\pi }\cdot \arctan (b/(a/2))=\frac{180°}{\pi }\cdot \arctan (0.134/(1/2))=15{}^{\circ } \\ x=90-60/2-y=90-60/2-15=45^{\circ } \end{gathered}$$

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