To answer the first question, we need to identify the side opposite ∠A in triangle ABC and the hypotenuse.
In triangle ABC:
- Side AB = 6 (adjacent to angle C)
- Side BC = 8 (adjacent to angle A)
- Side CA = 10 (hypotenuse)
In this case, side BC is opposite to angle A. Therefore, side BC = 8 is opposite to angle A.
Now let's find the ratio of the side opposite ∠A (BC = 8) to the hypotenuse (CA = 10):
\[ \text{Ratio} = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{8}{10} = \frac{4}{5} \]
The ratio in tenths is:
\[ \frac{4}{5} = 0.8 = \frac{8}{10} \text{ tenths} \]
So the answer is 8/10 tenths.
For the second question, we need to identify the location of ∠A' in triangle A'B'C'.
In triangle A'B'C':
- Side lengths are A'B' = 32, B'C' = 40, and C'A' = 24.
Since the lengths correspond to those in triangle ABC, we can determine that:
- The longest side in triangle A'B'C', which is B'C' = 40, is the hypotenuse.
- Therefore, side C'A' (24) corresponds to side AB (6), and side A'B' (32) corresponds to side BC (8).
In this arrangement, angle A' is opposite B'C' (the hypotenuse) and adjacent to A'B' (32) and C'A' (24).
Thus, angle A' is opposite the side length 32.
So, the answer is opposite the side length 32.
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