First, let's determine the ratio of the opposite side to the hypotenuse for triangle ABC.
In triangle ABC:
- The side opposite angle A is BC = 24.
- The hypotenuse is AC = 25.
Now, we calculate the ratio:
\[ \text{Ratio} = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{BC}{AC} = \frac{24}{25} = 0.96 \]
Next, we look at triangle A'B'C', which has side lengths 50, 14, and 48. We identify which side corresponds to the hypotenuse and which side corresponds to the opposite side of angle A'.
For triangle A'B'C':
- The hypotenuse should be the longest side, which is 50.
- Hence, the sides are:
- A'B' = 48 (one leg)
- A'C' = 14 (the other leg)
Since A' corresponds to angle A in triangle ABC and we have calculated the ratio to be 0.96, the opposite side in triangle A'B'C' must relate to the same ratio according to the dimensions of triangle ABC.
Since the ratio from triangle ABC (0.96) corresponds to the opposite side BC (which is 24), when we scale this ratio to triangle A'B'C', the side that is opposite angle A' should be the larger leg, which is 48.
Now, comparing to the options provided:
- The ratio of the opposite side to the hypotenuse is 0.96, and point A' is opposite the side that has length 48.
Thus, the correct alignment is:
- The ratio of the opposite side to the hypotenuse is 0.96, and point A' is opposite the side that has length 48.
The correct answer is: The ratio of the opposite side to the hypotenuse is 0.96, and point A' is opposite the side that has length 48.