A3. In a rectangle, one side measures $24 \mathrm{~cm}$, and the other is $8 \mathrm{~cm}$ shorter than the diagonal. Calculate the angle between the diagonal and the given side to the nearest minute.
(A) $70^{\circ} 31^{\prime}$
(B) $36^{\circ} 52^{\prime}$
(C) $53^{\circ} 13^{\prime}$
(D) $53^{\circ} 08^{\prime}$
(E) none of the above
A3. Let $x$ be the length of the diagonal. For the sides and the diagonal, we can write the Pythagorean theorem as $24^{2}+$ $(x-8)^{2}=x^{2}$, from which it follows that $x=32$. The angle $\varphi$ between the diagonal and the given side satisfies $\cos \varphi=\frac{24}{32}$, so $\varphi=\arccos \frac{24}{32}=53^{\circ} 08^{\prime}$.