Final answer:
The height of a sector with a 60-degree angle and adjacent leg of 12 units is found using the properties of a 30-60-90 triangle, resulting in the height being 6√3 units. Option A.
Step-by-step explanation:
To find the height of a sector with a 60-degree angle and an adjacent leg of 12 units, you can use properties of 30-60-90 triangles. This type of triangle has sides in the ratio of 1:√3:2. Given that the adjacent leg of the sector (which corresponds to the hypotenuse in our case) is 12 units, we can deduce the following:
The side opposite the 30-degree angle (short leg) is half the hypotenuse, so it is 6 units.
The side opposite the 60-degree angle (long leg) follows the ratio, being the short leg multiplied by √3.
Therefore, the height (long leg) of the sector is 6 units multiplied by √3, which equals 6√3 units. Hence, the correct option is A) h = 6√3 units.