Final answer:
The base of a 30-60-90 triangle with a height of 12 yards is 16 yards, determined using the ratio of sides for a 30-60-90 triangle.
Step-by-step explanation:
The student is asking about the base of a 30-60-90 triangle given the height. In a 30-60-90 triangle, the sides have a specific ratio: the length of the side opposite the 30° angle (which is the shortest side or half the base for this type of triangle) is half the length of the hypotenuse, and the length of the side opposite the 60° angle (which is the height for this type of triangle) is √3/2 times the length of the shortest side. If the height is 12 yards, we can denote the shortest side as s, then the height is √3/2 * s. Translating the height to an equation, we have 12 = √3/2 * s. Solving for s, we have s = 12 / (√3/2), which simplifies to s = 8. Therefore, the base of the triangle is twice this length, or 16 yards.