Answer:
Option (D)
Step-by-step explanation:
By applying Sine rule in the right ΔABD,
Sin(A) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
Sin(60)° = [tex]\frac{\text{BD}}{\text{AB}}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\text{BD}}{7\sqrt{3}}[/tex]
BD = [tex]7\sqrt{3}\times \frac{\sqrt{3} }{2}[/tex]
= [tex]\frac{21}{2}[/tex]
Now by applying Cosine rule in the right ΔBDC,
Cos(45)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{\sqrt{2}}=\frac{\frac{21}{2}}{x}[/tex]
x = [tex]\frac{21}{2}\times \sqrt{2}[/tex]
x = [tex]\frac{21\sqrt{2}}{2}[/tex]
Therefore, Option (D) is the correct option.
