Right triangle ABC has side lengths AB=6 , BC=8 , and CA=10 . A second right triangle has corresponding vertices of A′ , B′ , and C′ , with side lengths of 32, 40, and 24. In 3–5 sentences, describe how to find the ratio of the side opposite ∠A to the hypotenuse of triangle ABC . Then use this ratio to identify the location of point A′ in the second right triangle.
To find the ratio of the side opposite ∠A to the hypotenuse of triangle ABC, divide the length of side AC by the length of side AB. The ratio is 10/6 = 5/3. To identify the location of point A′ in the second triangle, multiply the length of side AB′ by the ratio 5/3. Thus, the length of AB′ would be (5/3) * 6 = 10.
