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

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

Answer 1

Opposite side to ∠A is BC = 24 and hypotenuse AC = 25, so the ratio = 24/25 = 0.96.
In the second triangle the hypotenuse is 50, so the side opposite A′ = 0.96·50 = 48. Thus A′ is opposite the side of length 48.