In a triangle the length of the side opposite the angle which measures 60° is 6√3 cm. What is the length of the side opposite to the angle which measures 90°?

In the given triangle, two angles are 90° and 60°, => Third angle = 30°

In a 30-60-90 triangle, the hypotenuse is always twice as long as the side opposite the 30° angle and the side opposite the 60° angle is √3 times as long as the side opposite the 30° angle.

The ratio of sides opposite 30°, 60° and 90° angles =1 : $$\sqrt{3}$$ : 2

Length of the side opposite the 60° angle = 6√3 cm

=> Length of side opposite the 90° angle = $$\frac{2}{\sqrt{3}} \times 6\sqrt{3} = 12$$ cm

=> Ans - (C)