In a certain right-angled triangle, the sides form an arithmetic progression, the area $t=486 \mathrm{dm}^{2}$; determine its sides and angles.
Let the two legs be denoted by $(a-d)$, and the hypotenuse by $(a+d)$. Then,

$$
(a-d)^{2}+a^{2}=(a+d)^{2}
$$

or

$$
a=4 d
$$

Furthermore,

$$
a(a-d)=12 d^{2}=2 \cdot 486
$$

which means

$$
d=9
$$

thus

$$
a=36 \mathrm{dm}, \quad a-d=27 \mathrm{dm} \quad \text { and } \quad a+d=45 \mathrm{dm}
$$

If the angle opposite to the side $a$ is $\alpha$, then

$$
\sin \alpha=\frac{4}{5} \quad \text { and thus } \quad \alpha=53^{\circ} 7^{\prime} 48^{\prime \prime}
$$

(Sándor Pichler, Budapest.)

The problem was also solved by: L. Bánó, F. Eckhart, V. Eckstein, M. Fekete, H. Friedländer, P. Füstös, Z. Harsányi, P. Heimlich, Gy. Jánosy, J. Kiss, B. Koffler, B. Lázár, K. Miklóssy, L. Neumann, S. Petrik, Z. Reich, E. Sárközy, Gy. Schuster, J. Steiger, B. Tóth, V. Wáhl, J. Winkler.