Triangle ABC is a right triangle with its right angle at B.
Thus,
is the hypotenuse of right triangle ABC, and
A and
B are the legs of right triangle ABC.
By the Pythagorean theorem,
AB=√202−162=√400−256=√144=12
Since triangle DEF is similar to triangle ABC,
with vertex F corresponding to vertex C, the measure of angleF equals the measure of angle C.
Thus, sin F = sin C.
From the side lengths of triangle ABC,
Therefore,
sinF=.
Either
or its decimal equivalent or its decimal equivalent,
6 may be gridded as the correct answer.