Question

Right triangle ABC
has side lengths AB=7
, BC=24
, and AC=25
. A second right triangle, A′B′C′
, has side lengths of 50, 14, and 48. Find the ratio of the side opposite ∠A
to the hypotenuse of triangle ABC
. Use this ratio to identify the location of point A′
in the second right triangle.(1 point)
Responses

The ratio of the opposite side to the hypotenuse is 0.28, and point A′
is opposite the side that has length 14.
The ratio of the opposite side to the hypotenuse is 0.28, and point upper A prime is opposite the side that has length 14.

The ratio of the opposite side to the hypotenuse is 1.04, and point A′
is opposite the side that has length 48.
The ratio of the opposite side to the hypotenuse is 1.04, and point upper A prime is opposite the side that has length 48.

The ratio of the opposite side to the hypotenuse is 0.96, and point A′
is opposite the side that has length 48.
The ratio of the opposite side to the hypotenuse is 0.96, and point upper A prime is opposite the side that has length 48.

The ratio of the opposite side to the hypotenuse is 0.96, and point A′
is opposite the side that has length 14.

Answer 1

To find the ratio of the side opposite \( \angle A \) to the hypotenuse of triangle \( ABC \), we first identify the sides and angles based on the problem statement.

In triangle \( ABC \):
- The side opposite \( \angle A \) is \( BC \) (24).
- The hypotenuse \( AC \) is 25.

Now, we can calculate the ratio:

\[
\text{Ratio} = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{BC}{AC} = \frac{24}{25}
\]

Calculating this gives:

\[
\frac{24}{25} = 0.96
\]

Now, for triangle \( A'B'C' \) with side lengths \( 50, 14, \) and \( 48 \):
- The side opposite \( A' \) corresponds to \( 14 \).
- The hypotenuse is \( 50 \).

So we have:

\[
\text{A' location} = \text{opposite side length} = 14
\]

Since we established the ratio from triangle \( ABC \) as \( 0.96 \), and that the side \( A' \) is opposite the side of length \( 14 \):

- The ratio of the opposite side to the hypotenuse is \( 0.96 \), and point \( A' \) is opposite the side that has length \( 14 \).

Thus, 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.**