To find the ratio of the side opposite ∠A to the hypotenuse of triangle ABC, we first identify which sides correspond to these angles in triangle ABC:
- The side opposite ∠A (which is angle A) is side BC = 24.
- The hypotenuse AC in triangle ABC is 25.
Now, we can calculate the ratio:
\[ \text{Ratio} = \frac{\text{Opposite side}}{\text{Hypotenuse}} = \frac{BC}{AC} = \frac{24}{25} = 0.96 \]
Next, we will compare this ratio to the second triangle A′B′C′. The sides of triangle A′B′C′ are 50, 14, and 48. Here:
- The hypotenuse is the longest side, which is 50.
- The side opposite ∠A′ should be identified, and we'll consider the sides in ascending order, which correspond to the angles.
Since the sides of triangle A′B′C′ are 14 (shortest), 48 (medium), and 50 (hypotenuse), we can see that if the 14 is opposite the smallest angle (∠A′), then we match the ratios.
Given that we consider the ratio of opposite side to hypotenuse, our previous determination was that the point corresponding to angle A′ should be opposite the side that has the same relationship as triangle ABC's opposite side to the hypotenuse.
Using the same ratio, we find that since in triangle A′B′C′:
\[ \text{Ratio for A' (opposite 14)} = \frac{14}{50} \]
Calculating \( \frac{14}{50} = 0.28 \), we see that this 0.28 does not match the 0.96 we calculated for triangle ABC.
Thus, point A' must be placed such that it corresponds to the structure of opposite related to the angles.
Therefore:
- The correct ratio is \(0.96\), and point A′ is opposite the side that has length \(48\).
None of the options specify the angle-related criteria correctly but based on the problem statement and the calculations you've shown, the response we can conclusively say is that:
The ratio of the opposite side to the hypotenuse is 0.96, and point A′ is opposite the side that has length 48.