To find the ratio of the side opposite ∠A to the hypotenuse of triangle ABC, we first identify the sides of triangle ABC:
- Side lengths:
- \( AB = 9 \) (opposite to vertex C)
- \( BC = 12 \) (opposite to vertex A)
- \( AC = 15 \) (the hypotenuse)
The side opposite ∠A in triangle ABC is BC, which measures 12. The hypotenuse is AC, which measures 15. Now, we can compute the ratio:
\[ \text{Ratio} = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{BC}{AC} = \frac{12}{15} = \frac{4}{5} = 0.8 \]
Now, we can move to triangle A′B′C′, which has the following side lengths:
- Side lengths:
- \( A'B' = 30 \)
- \( B'C' = 24 \)
- \( A'C' = 18 \) (hypotenuse)
The side opposite corresponding vertex A′ in triangle A′B′C′ would be the side B′C′, which has a length of 24.
Thus, the information concludes as follows:
- The ratio of the opposite side to the hypotenuse in triangle ABC is \( 0.8 \).
- Point A′ in triangle A′B′C′ is opposite the side that has length \( 24 \).
Therefore, the correct response is:
The ratio of the opposite side to the hypotenuse is 0.8, and point A′ is opposite the side that has length 24.
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