Answer: 77/85
Step-by-step explanation:
Triangles HIG and FED are similar triangles. We know this because we have two pairs of angles that are congruent (angle G = angle D; angle I = angle E). Use the AA (angle angle) similarity theorem.
Since angles G and D are congruent, computing sin(D) is equivalent to finding sin(G)
sin(angle) = opposite/hypotenuse
sin(G) = IH/HG
sin(G) = 77/85
sin(D) = 77/85