The diagram below represent the information given in the question
From the diagram
[tex]\begin{gathered} AD=9ft \\ DC=23ft \\ <\text{ADC}=80^0 \\ AC=d=\text{diagonal} \end{gathered}[/tex]The diagonal of the trapezoid can be calculated using cosine rule as shown below:
[tex]d^2=AD^2+DC^2-2\times AD\times DC\times\cos D[/tex][tex]d^2=9^2+23^2-2\times9\times23\times\cos 80^0[/tex][tex]\begin{gathered} d^2=81+529-414\times0.1736 \\ d^2=610-71.80 \\ d^2=538.10965 \end{gathered}[/tex][tex]\begin{gathered} d=\sqrt[]{538.10965} \\ d=23.197 \\ d\approx23ft \end{gathered}[/tex]Hence, the length of the diagonal is 23ft, OPTION C
