Answer:
DF = 17.12
Step-by-step explanation:
From the picture attached,
From ΔABC and ΔEFD,
m∠ABC = m∠EFD = 28°
m∠BAC = m∠EDF = 68°
By AA property of similarity, ΔABC and ΔEFD will be similar.
And their corresponding sides will be proportional.
[tex]\frac{AB}{EF}=\frac{BC}{DF}=\frac{AC}{ED}[/tex]
[tex]\frac{4}{EF}=\frac{BC}{DF}=\frac{2}{8}[/tex]
[tex]\frac{4}{EF}=\frac{1}{4}[/tex]
EF = 16
Now by applying cosine rule in ΔDEF,
DF² = ED² + EF² - 2(ED)(EF)cos(E)
DF² = 8² + (16)² - 2(8)(16)cos(84)°
DF² = 320 - 26.76
DF = √(293.24)
DF = 17.12
