In a triangle the length of the side opposite the right angle is 9√3 cm, what is the length of the side opposite to the angle which measures 30 degree?

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

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 90° angle = $$9\sqrt{3}$$ cm

=> Length of side opposite the 30° angle = $$\frac{9\sqrt{3}}{2}$$ cm

=> Ans - (D)