Final answer:
In a 30-60-90 triangle, if the side opposite the 60 degree angle is 12 centimeters, the length of the side opposite the 30 degree angle is approximately 6.93 centimeters.
Step-by-step explanation:
When dealing with a 30-60-90 triangle, there is a set ratio between the lengths of the sides. The side opposite the 30° angle is the shortest side, also known as half the length of the hypotenuse. The side opposite the 60° angle is √3 times the length of the side opposite to the 30° angle. In this case, the length of the side opposite the 60° angle is given as 12 centimeters.
To find the length of the side opposite the 30° angle, we simply divide the length of the side opposite the 60° angle by √3. So the calculation would be:
Length of the side opposite 30° = Length of the side opposite 60° / √3
Length of the side opposite 30° = 12 cm / √3
Length of the side opposite 30° = 12 cm / 1.732
Length of the side opposite 30° ≈ 6.93 cm
The length of the side opposite the 30° angle is approximately 6.93 centimeters.