Answer:
C
Step-by-step explanation:
The base angles are congruent, both 60°, thus the triangle is isosceles and x is a perpendicular bisector ( divides the base into 6 and 6 )
Using the tangent ratio in the right triangle on the left and exact value
tan60° = [tex]\sqrt{3}[/tex] , then
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{6}[/tex] ( multiply both sides by 6 )
6 × tan60° = x , that is
x = 6[tex]\sqrt{3}[/tex]
Using the cosine ratio in the same right triangle and exact value
cos60 = [tex]\frac{1}{2}[/tex] , then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{y}[/tex] ( multiply both sides by y )
y × cos60° = 6 , that is
y × [tex]\frac{1}{2}[/tex] = 6 ( multiply both sides by 2 )
y = 12
