4. A trapez has the following data: $a=7, b=4, c=3$ and $\beta=90^{\circ}$. Calculate the angle between the diagonals of the trapezoid to the nearest hundredth of a degree.
4. Let $\varphi=\angle B A C$ and $\varepsilon=\angle A B D=\angle B D C$. In the right triangles $A B C$ and $B C D$, we get $\operatorname{tg} \varphi=\frac{4}{7}$ and $\operatorname{tg} \varepsilon=\frac{4}{3}$, so $\varphi=29.74^{\circ}$ and $\varepsilon=53.13^{\circ}$, and $\angle A E B=97.13^{\circ}$. The angle between the diagonals is $82.87^{\circ}$.

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Sketch with the intersection of the diagonals $\mathrm{E}$ marked and

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