A3. The lengths of the sides of a triangle are $a=5, b=3$ and $c=4$. The angle $\alpha$ measures:
(A) $60^{\circ}$
(B) $89^{\circ}$
(C) $91^{\circ}$
(D) $180^{\circ}$
(E) none of the above
A3. We use the cosine rule to calculate the angle $\alpha: \cos \alpha=\frac{b^{2}+c^{2}-a^{2}}{2 b c}=\frac{9+16-25}{24}=0$. Therefore, the angle $\alpha$ is a right angle. The correct answer is E.