S.102 T.267

$9^2=6^2+8^2-2\cdot6\cdot8\cdot\cos\alpha$

$81=100-96\cdot\cos\alpha$
$-19=-96\cdot\cos\alpha$
$96\cdot\cos\alpha=19$
$\alpha=78{,}584...\approx78{,}58°$
$\frac{8}{\sin\beta}=\frac{9}{\sin\ 78{,}58}$
$\sin\beta=\frac{8\cdot\sin78{,}58}{9}$
$\sin\beta=0{,}8712...$
$\beta=60{,}598...\approx60{,}60°$
$180°-\left(78{,}58°+60{,}60°\right)=40{,}82°$

78,58 > 60,60 > 40,82
$V:\ 78{,}58°\ \left(∢\alpha\right)$