Tomi's Challenges - #2

The sine theorem is given by: $\newline$

$\frac{\sin(\alpha)}{a}=\frac{\sin(\beta)}{b}$

\since the angle is acute, we can take the natural log on both sides. After taking the natural log, and transforming the expressions, we get $\newline$

$\ln(\sin(\alpha))-\ln(\sin(\beta))=\ln(a)-\ln(b)$ , that is; $\newline$ $\ln(\sin(\alpha))-\ln(\sin(\beta))=-6$ .

After squaring both sides, we get $\newline$

$\ln^2(\sin(\alpha))-2\ln(\sin(\alpha))\ln(\sin(\beta))+\ln^2(\sin(\beta)=36$

$-2\ln(\sin(\alpha))\ln(\sin(\beta))=34$

$\ln(\sin(\alpha))\ln(\sin(\beta))=-17$