Question

Right triangle ABC
𝐴
𝐵
𝐶
has side lengths AB=9
𝐴
𝐵
=
9
, BC=12
𝐵
𝐶
=
12
, and AC=15
𝐴
𝐶
=
15
. A second right triangle, A′B′C′
𝐴
′
𝐵
′
𝐶
′
, has side lengths of 30, 24, and 18. Find the ratio of the side opposite ∠A
∠
𝐴
to the hypotenuse of triangle ABC
𝐴
𝐵
𝐶
. Then use this ratio to identify the location of point A′
𝐴
′
in the second right triangle.(1 point)
Responses

The ratio of the opposite side to the hypotenuse is 1.25, and point A′
𝐴
′
is opposite the side that has length 24.
The ratio of the opposite side to the hypotenuse is 1.25, and point upper A prime is opposite the side that has length 24.

The ratio of the opposite side to the hypotenuse is 0.8, and point A′
𝐴
′
is opposite the side that has length 18.
The ratio of the opposite side to the hypotenuse is 0.8, and point upper A prime is opposite the side that has length 18.

The ratio of the opposite side to the hypotenuse is

Answer 1

Opposite ∠A is BC = 12 and the hypotenuse is AC = 15, so the ratio is 12/15 = 4/5 = 0.8. In the second triangle the hypotenuse is 30, so the side opposite A′ is 0.8·30 = 24 — A′ is opposite the side of length 24.