Answer:
a = 2[tex]\sqrt{3}[/tex] , c = 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the tangent ratio in the right triangle and the exact value
tan30° = [tex]\frac{\sqrt{3} }{3}[/tex] , then
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{a}{b}[/tex] = [tex]\frac{a}{6}[/tex] = [tex]\frac{\sqrt{3} }{3}[/tex] ( cross- multiply )
3a = 6[tex]\sqrt{3}[/tex] ( divide both sides by 3 )
a = 2[tex]\sqrt{3}[/tex]
Using Pythagoras' identity in the right triangle
c² = 6² + (2[tex]\sqrt{3}[/tex] )² = 36 + 12 = 48 ( take square root of both sides )
c = [tex]\sqrt{48}[/tex] = [tex]\sqrt{16(3)}[/tex] = 4[tex]\sqrt{3}[/tex]
