Final answer:
The correct set of values for the side lengths of a 30-60-90 triangle is Option C: {4, 4√3, 8}, where the sides adhere to the specific ratios characteristic of a 30-60-90 triangle.
Step-by-step explanation:
The question asks which set of values could be the side lengths of a 30-60-90 triangle. In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg, which is opposite the 30-degree angle, and the length of the longer leg, opposite the 60-degree angle, is the shorter leg length multiplied by the square root of 3 (√3). Comparing the given options, the correct set must adhere to these ratios.
Let's analyze each option:
- A. {4, 4√2, 8} - Incorrect, as 4√2 does not equal 2√3 times 4.
- B. {4, 4.2, 8} - Incorrect, since 4.2 is not in the proper ratio with 4 or 8.
- C. {4, 4√3, 8} - Correct, as 4√3 is exactly 4 times √3, and the hypotenuse 8 is twice the shorter leg 4.
- D. {4, 4 /3, 8} - Incorrect, as 4/3 does not satisfy the ratio with 4 or 8.
Therefore, the set of values that could be the side lengths of a 30-60-90 triangle is Option C: {4, 4√3, 8}.