Answer:
x = 19.6
Step-by-step explanation:
By applying cosine rule in ΔBCD,
cos(30)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{BC}{BD}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{BC}{16}[/tex]
BC = [tex]8\sqrt{3}[/tex]
Now, by applying sine rule in ΔBAC,
sin(45)° = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{\sqrt{2}}=\frac{AB}{BC}[/tex]
[tex]\frac{1}{\sqrt{2}}=\frac{x}{8\sqrt{3}}[/tex]
x = [tex]8\sqrt{6}[/tex]
x = 19.59
x ≈ 19.6
