Answer:
a = 15
b = 5(6 - √3)
Step-by-step explanation:
Construction to be done in the given figure → Drop a perpendicular line (DE) from D to line AB.
From ΔAED,
cos(60°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{AE}{AD}[/tex]
cos(60°) = [tex]\frac{AE}{10\sqrt{3}}[/tex]
[tex]\frac{1}{2}=\frac{AE}{10\sqrt{3}}[/tex]
AE = [tex]5\sqrt{3}[/tex]
Since, b = AB - AE
b = (30 - 5√3)
b = 5(6 - √3)
By sine rule,
sin(60°) = [tex]\frac{\text{Oppositet side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{a}{10\sqrt{3}}[/tex]
a = [tex]\frac{30}{2}[/tex]
a = 15
