A) 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 angle A to the hypotenuse of triangle ABC. Then use this ratio to identify the location of point A' in the second right triangle. (1 point) The ratio of the opposite side to the hypotenuse is 3/5 and point is opposite the side that has length 24. The ratio of the opposite side to the hypotenuse is 4/3 and point is opposite the side that has length 40. The ratio of the opposite side to the hypotenuse is 4/5 and point is opposite the side that has length 32.

Question

GPT-4o mini · Answer

To find the ratio of the side opposite angle A to the hypotenuse of triangle ABC, we first identify the lengths of the sides: AB = 6 (opposite side), AC (hypotenuse) = 10. We then calculate the ratio as 6/10, which simplifies to 3/5. With this ratio, we look at the corresponding side lengths in the second triangle, where the hypotenuse is 40 (the longest side).

Using the ratio of 3/5, we can set up the equation: opposite side / hypotenuse = 3/5. Let the opposite side be x. Thus, \( x / 40 = 3/5 \), which leads us to find \( x = (3/5) * 40 = 24 \). Therefore, point A' is located opposite the side of length 24 in triangle A'B'C'.