A certain right-angled triangle has an area of $1470 \mathrm{~m}^{2}$, the ratio of the sides is $a: b: c=13: 12: 5$; find the sides individually and the two acute angles.
$a=91 \mathrm{~m}, \quad b=84 \mathrm{~m}, \quad c=35 \mathrm{~m}, \quad \beta=67^{\circ} 22^{\prime} 48^{\prime \prime}, \quad \gamma=22^{\circ} 37^{\prime} 12^{\prime \prime}$.