Use the Law of Sines to find the length of DE to the nearest tenth of an inch. (Enter only the number.)

So angle FED is $${\mathtt{180}}{\mathtt{\,-\,}}{\mathtt{45}}{\mathtt{\,-\,}}{\mathtt{63}} = {\mathtt{72}}$$

The Sine rules states that sinD/d = sinE/e = sinF/f, where the lowercase letter is the side opposite to the angle in captials.

sinE/3.8=sinF/DE

$${\frac{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{72}}^\circ\right)}}{{\mathtt{3.8}}}} = {\mathtt{0.250\: \!278\: \!030\: \!603\: \!947\: \!4}}$$

$${\frac{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{72}}^\circ\right)}}{{\mathtt{3.8}}}} = {\frac{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{45}}^\circ\right)}}{{\mathtt{x}}}}$$

$${\mathtt{x}} = {\frac{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{45}}^\circ\right)}}{{\mathtt{0.250\: \!278\: \!030\: \!603\: \!947\: \!4}}}} \Rightarrow {\mathtt{x}} = {\mathtt{2.825\: \!285\: \!061\: \!899\: \!665\: \!9}}$$

Round this to the nearest tenth of an inch and that would be 2.8 inches.