6 + 8 > x ~ $(Triangle inequality)$
x < 14
Similarly,~ x + 6 > 8
x > 2
\therefore 2 < x < 14
$By the cosine rule, $ cos\alpha = \frac{100 - x^2}{96}
$If $ cos\alpha > 0, $ this means that $ 0 < \alpha < \frac{\pi}{2}
\frac{100 - x^2}{96} > 0
x^2 - 100 < 0
\therefore 0 < x < 10, x...