To find the ratio of the side opposite ∠A to the hypotenuse of triangle ABC, we first identify the lengths of each side of triangle ABC:
- AB = 7 (which is opposite ∠C)
- BC = 24 (which is opposite ∠A)
- AC = 25 (the hypotenuse)
The side opposite ∠A is BC, which has the length of 24. The hypotenuse AC has the length of 25.
Now, we calculate the ratio of the opposite side to the hypotenuse:
\[ \text{Ratio} = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{BC}{AC} = \frac{24}{25} = 0.96 \]
Next, we consider the second triangle A′B′C′ with the given side lengths of 50, 14, and 48.
In triangle A′B′C′:
- Let's identify the hypotenuse. The longest side is 50, so that's our hypotenuse.
- The sides opposite the angles will be 14 and 48.
Since we have established that the ratio from triangle ABC is 0.96, we now need to find a corresponding angle in triangle A′B′C′ where this ratio holds.
We compare the opposite sides with the hypotenuse:
- For side 14: \[ \text{Ratio} = \frac{14}{50} = 0.28 \]
- For side 48: \[ \text{Ratio} = \frac{48}{50} = 0.96 \]
From this calculation, we find that the ratio corresponding to ∠A in triangle A′B′C′ is the side opposite the angle that has the length 48 (since 0.96 matches the ratio we calculated).
Thus, we summarize our findings:
- The ratio of the opposite side to the hypotenuse is 0.96.
- Point A′ in triangle A′B′C′ is opposite the side that has length 48.
Putting this all together, the correct response is:
The ratio of the opposite side to the hypotenuse is 0.96, and point A′ is opposite the side that has length 48.