Calculate the sides $a, b$, and $c$ of any triangle $ABC$, if the angles of the triangle $A, B$, and $C$ and the area of the triangle $T$ are given.
Minthogy

$$
\begin{aligned}
a b & =\frac{2 T}{\sin C} \\
\frac{a}{b} & =\frac{\sin A}{\sin B}
\end{aligned}
$$

it follows that

$$
a^{2}=\frac{2 T \sin A}{\sin B \sin C}
$$

similarly

$$
\begin{aligned}
b^{2} & =\frac{2 T \sin B}{\sin C \sin A} \\
c^{2} & =\frac{2 T \sin C}{\sin A \sin B}
\end{aligned}
$$

The values of \(a\), \(b\), and \(c\) can be obtained by a simple square root from the last three equations.

(The problem was solved by: János Breznyik, a student at Selmeczbánya).

The problem was also solved by: Domokos Berzenczey, 7th grade real school, Déva; Béla Bolemann, 8th grade evangelical gymnasium, Budapest; Richárd Engel, 7th grade real school, Györ; Ármin Fried, 7th grade real school, Déva; Gusztáv Grossmann, 8th grade evangelical gymnasium, Budapest; Róbert Hertzka, 8th grade evangelical gymnasium, Budapest; Tivadar Heymann, 8th grade real school, Györ; Ármin Hirschler, 8th grade real school, Györ; János Imre, 8th grade gymnasium, Nyíregyzáza; György Jankovics, 8th grade state gymnasium, Losoncz; Gergely Jorga, Gilád; Jenő Kis, Budapest; Elemér Meitner, 8th B grade real school, 5th district, Budapest; Viktor Müller, 8th grade evangelical gymnasium, Budapest; Ignácz Pilczer, 8th grade gymnasium, Kaposvár; József Rothschild, 8th grade real school, Györ; József Rosenberg, 8th grade real school, Györ; Jenö Schiller, 7th grade real school, Györ; Gábor Schulgof, 8th grade real school, Pécs; Sándor Suták, 8th grade gymnasium, Nyíregyháza; Gusztáv Szabó and Jenő Unger, 7th grade real school, Györ; Aladár Visnya, 7th grade real school, Ferencz Zsaborszky, 7th grade real school, Pécs.