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 te 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, we can divide the length of side CA by the length of side AB. Therefore, the ratio is 10/6 = 5/3.
Using this ratio in the second right triangle, we can identify the location of point A'. Since the hypotenuse of this triangle is 40, we can multiply the ratio 5/3 by 40, obtaining (5/3)*40 = 200/3. Therefore, the side opposite A' in the second triangle has a length of 200/3.