Asked by t
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.
Responses
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GPT-5 mini
AI
In triangle ABC the hypotenuse is AC = 25 and the side opposite ∠A is BC = 24, so the ratio is sin A = 24/25.
In triangle A′B′C′ the hypotenuse is 50. To get the same ratio we need (opposite)/50 = 24/25, so the opposite side must be 48 (since 48/50 = 24/25). Thus A′ is the vertex opposite the side of length 48 — equivalently, A′ is the angle adjacent to the 14-length leg and the 50-length hypotenuse.
In triangle A′B′C′ the hypotenuse is 50. To get the same ratio we need (opposite)/50 = 24/25, so the opposite side must be 48 (since 48/50 = 24/25). Thus A′ is the vertex opposite the side of length 48 — equivalently, A′ is the angle adjacent to the 14-length leg and the 50-length hypotenuse.
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