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 0.96, 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 0.28, 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 14.

Answer 1

In triangle ABC, we have:

- AB = 7 (opposite side relative to angle A)
- AC = 25 (hypotenuse)
- BC = 24 (adjacent side relative to angle A)

To find the ratio of the side opposite angle A (AB) to the hypotenuse (AC), we calculate:

\[
\text{Ratio} = \frac{\text{Opposite Side}}{\text{Hypotenuse}} = \frac{AB}{AC} = \frac{7}{25}
\]

Now we can compute this fraction:

\[
\frac{7}{25} = 0.28
\]

Next, we want to use this ratio to identify the location of point A' in the second right triangle A'B'C'.

In triangle A'B'C', the side lengths are:

- A'B' = 14 (opposite to angle A')
- A'C' = 50 (hypotenuse)
- B'C' = 48 (adjacent to angle A')

Now we will find the ratio of the side opposite angle A' (A'B') to the hypotenuse (A'C'):

\[
\text{Ratio} = \frac{A'B'}{A'C'} = \frac{14}{50}
\]

Calculating this gives:

\[
\frac{14}{50} = 0.28
\]

Since both triangles have the same ratio (0.28), point A' in triangle A'B'C' must be opposite the side that corresponds to side AB in triangle ABC, which is the side with length 14.

Thus, the correct response is:

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