Final answer:
The correct option for the side lengths of a 30-60-90 triangle is (c) {4, 4√3, 8}, as it follows the ratio of 1:√3:2, which is characteristic for this type of right triangle.
Step-by-step explanation:
The question is about determining which set of values could represent the side lengths of a 30-60-90 triangle. A 30-60-90 triangle is a special right triangle with angles of 30 degrees, 60 degrees, and 90 degrees. The ratios of the sides opposite these angles are always 1:√3:2. This means that the side opposite the 30-degree angle is x units in length, the side opposite the 60-degree angle is x√3 units in length, and the hypotenuse is 2x units in length.
Looking at the options provided in the question:
- Option (a): {4, 4√2, 8√2} does not follow the 1:√3:2 ratio.
- Option (b): {4, 4√3, 8√3} also does not match the expected ratio.
- Option (c): {4, 4√3, 8} correctly matches the ratio of 1:√3:2, with x being 4.
- Option (d): {4, 4√2, 8} does not meet the specific ratio for a 30-60-90 triangle.
Therefore, the correct set of side lengths for a 30-60-90 triangle from the given options is (c) {4, 4√3, 8}.