Question

Right triangle ABC 𝐴 𝐵 𝐶 has side lengths AB=6 𝐴 𝐵 = 6 , BC=8 𝐵 𝐶 = 8 , and CA=10 𝐶 𝐴 = 10 . A second right triangle has corresponding vertices of A′ 𝐴 ′ , B′ 𝐵 ′ , and C′ 𝐶 ′ , with side lengths of 32, 40, and 24. In 3–5 sentences, describe how to 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.(4 points) simple and basic

Answer 1

In triangle ABC the hypotenuse is CA = 10 and the side opposite ∠A is BC = 8, so the ratio (opposite/hypotenuse) = 8/10 = 4/5. In the second triangle the hypotenuse is the longest side, 40, so the side opposite A′ must be (4/5)·40 = 32. Thus A′ is the vertex opposite the side of length 32 (the other two vertices are joined by the 32-length side).