Question

find the sine of angle H

there are two similar right triangles, one has unknown lengths and angles which are classified as H, F, G, the other triangle has Line ED which has a length of 20, Line EC which has a length of 52, and Line DC which has a length of 48

Angle H corresponds with angle C

Answer 1

Since the triangles are similar and H corresponds to C, sin(H) = sin(C).

In triangle EDC, the hypotenuse is EC = 52 and the side opposite angle C is ED = 20, so
sin(C) = opposite/hypotenuse = 20/52 = 5/13.

Therefore sin(H) = 5/13.