# Square Trapped in Pentagon

Geometry Level 4

The square $$\color{blue}{\text{PQRS}}$$ is inscribed in the regular pentagon $$\color{red}{\text{ABCDE}}$$ as shown.

If the side length of the pentagon is $$\,a$$ and the side length of the square is $$\,b$$, then the ratio of $$\;\dfrac{a}{b}$$ can be expressed as $$\,\Psi\sin\Theta+\tan\Phi$$, where $$\Theta$$ and $$\Phi$$ are in degrees. Find the value of $$\;\Psi+\Theta+\Phi$$.

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