First, we need to find the ratio of the side opposite ∠A to the hypotenuse of triangle ABC.
In triangle ABC:
- Side opposite to angle A (BC) = 24
- Hypotenuse (AC) = 25
Now, we calculate the ratio:
\[ \text{Ratio} = \frac{\text{Opposite side}}{\text{Hypotenuse}} = \frac{BC}{AC} = \frac{24}{25} \]
Calculating this gives:
\[ \text{Ratio} = \frac{24}{25} = 0.96 \]
Now, we identify the location of point \( A' \) in triangle \( A'B'C' \). The side lengths of triangle \( A'B'C' \) are given as 50, 14, and 48.
To find the correct side opposite point \( A' \), we can look at which of the given sides correspond to the ratios derived from triangle ABC. In triangle \( A'B'C' \):
- The longest side must be the hypotenuse (50), and
- The side opposite \( A' \) should match the ratio previously calculated.
Since we calculated \( \frac{24}{25} \), the side lengths in triangle \( A'B'C' \) must be scaled accordingly. The side opposite \( A' \) should be similar with the ratio of \( 24 \) to \( 25 \) and correspond to the proper side length.
Here, \( A' \) is opposite the side of length 14. Therefore:
- The ratio of the side opposite \( A' \) (which is 14) to the hypotenuse (which is 50) in triangle \( A'B'C' \) is:
\[ \frac{14}{50} = 0.28 \]
Thus, based on our findings:
- The ratio of the opposite side to the hypotenuse is \( 0.28 \).
- Point \( A' \) is opposite the side that has length 14.
Hence, the correct response is:
The ratio of the opposite side to the hypotenuse is 0.28, and point \( A' \) is opposite the side that has length 14.