To find the ratio of the side opposite ∠A to the hypotenuse of triangle ABC, we first need to identify the appropriate sides. In triangle ABC, the sides are:
- AB = 7 (opposite side to angle C)
- BC = 24 (opposite side to angle A)
- AC = 25 (hypotenuse)
The side opposite ∠A is BC, which is 24. The hypotenuse is AC, which is 25.
Now, we calculate the ratio of the opposite side to the hypotenuse:
\[ \text{Ratio} = \frac{BC}{AC} = \frac{24}{25} = 0.96 \]
Next, we need to identify the location of point A′ in the second right triangle \(A'B'C'\) with side lengths of 50, 14, and 48.
In triangle \(A'B'C'\):
- Let’s assume:
- One of the shorter sides (14) is opposite angle C' (the angle adjacent to the hypotenuse),
- The other shorter side (48) is opposite angle A' (the angle adjacent to the hypotenuse),
- The hypotenuse (50) is opposite angle B'.
The angle A' is opposite the side length 48.
Thus:
The ratio of the opposite side to the hypotenuse is \(0.96\), and point \(A'\) is opposite the side that has length \(48\).
This means 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.
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