Since you know the length of a side (side f) and the measure of its opposite angle (<F), you have enough information to establish the ratio used in the law of sides. Since you also know the measure of angle D, you can find side d.
[tex] \dfrac{f}{\sin F} = \dfrac{d}{\sin D} [/tex]
[tex] \dfrac{12~m}{\sin 40^\circ} = \dfrac{d}{\sin 100^\circ} [/tex]
[tex] d \sin 40^\circ = 12~m \sin 100^\cric [/tex]
[tex] d = \dfrac{12~m \sin 100^\circ}{\sin 40^\circ} [/tex]
[tex] d = 18.3850... m [/tex]
Answer: 18.4 m
