Answer and Explanation:
[tex]Greetings![/tex]
[tex]Let's~answer~your~question![/tex]
[tex]Triangle~ ABC ~is ~a ~right~ triangle~ with ~its~ right~ angle ~at ~B. ~Therefore,~AC\\is~ the~ hypotenuse~ of~ right~ triangle~ ABC,~ and~ AB ~and ~BC ~are~ the~ legs~ of~ right~\\ triangle ~ABC.[/tex]
[tex]According~ to~ the~ Pythagorean ~theorem,[/tex]
[tex]AB=\sqrt{20^2-16^2}=\sqrt{400-256}=\sqrt{144}=12[/tex]
[tex]Since ~triangle~DE[/tex][tex]F~is ~similar~ to~ triangle~ ABC,~ with~ vertex ~F ~corresponding~to~ vertex~ C,~ the~ measure\\ of~angle~ \angle F~equals~ the~ measure~ of~ angle~\angle C.[/tex]
[tex]Therefore,~ sinF=sinC. ~From ~the~ side~ lengths~ of ~triangle~ ABC,[/tex]
[tex]sinF=\frac{opposite ~side}{hypotenuse} =\frac{AB}{AC} =\frac{12}{20}=\frac{3}{5}[/tex]
[tex]Therfore, ~sinF=\frac{3}{5}~or~0.6[/tex]
