To find the ratio of the side opposite ∠A to the hypotenuse of triangle ABC, we first identify the sides:
- AB = 7 (opposite side to ∠C)
- BC = 24 (opposite side to ∠A)
- AC = 25 (hypotenuse)
We need the side opposite to ∠A, which is side BC (24), and the hypotenuse, which is side AC (25).
Now we calculate the ratio:
\[ \text{Ratio} = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{BC}{AC} = \frac{24}{25} = 0.96 \]
Now, we need to identify which side A′ is opposite in the triangle A′B′C′. We can identify the side lengths of triangle A′B′C′:
- 50 (hypotenuse of triangle A'B'C')
- 14 (shorter leg)
- 48 (longer leg)
Since triangle A′B′C′ is also a right triangle, we need to identify the side opposite the angle corresponding to angle A in triangle ABC.
Given the following relationships:
- The side opposite ∠A (which corresponds to BC in triangle ABC, the side of length 24) is represented by the side A′B′ of length 14 in triangle A′B′C′.
Thus, the ratio of the side opposite ∠A to the hypotenuse in triangle ABC is 0.96, and point A′ is opposite the side that has length 14.
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 14.