Let's begin by identifying key information given to us:
[tex]\begin{gathered} AC=b=8ft \\ AB=c=16ft \\ BC=a=17ft \\ \angle C=? \end{gathered}[/tex]
To obtain the angle C, we will use the Law of Cosines as shown below:
[tex]\begin{gathered} c^2=a^2+b^2-2ab\cdot cosC \\ We\text{ will make ''C'' the subject of the formula, we have:} \\ 2ab\cdot cosC=a^2+b^2-c^2 \\ cosC=\frac{a^2+b^2-c^2}{2ab} \\ a=8ft,b=16ft,c=17ft \\ cosC=\frac{16^2+8^2-17^2}{2\times8\times16}=\frac{256+64-289}{256}=\frac{31}{256} \\ cosC=0.121 \\ C=cos^{-1}(0.121)=83.05\approx83.1 \\ C=83.1^{\circ} \\ \\ \therefore C=83.1^{\circ} \end{gathered}[/tex]
