right triangle ABC has side lengths AB=9, BC=12 and AC=15. A second right triangle, A'B'C, has side lengths of 30,24,and 18. 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. the hypotenuse is 0.8
To find the ratio of the side opposite angle A to the hypotenuse of triangle ABC, we divide the length of the side opposite angle A by the length of the hypotenuse.
In triangle ABC, the side opposite angle A is BC, which has a length of 12. The hypotenuse of triangle ABC is AC, which has a length of 15.
Therefore, the ratio of the side opposite angle A to the hypotenuse of triangle ABC is 12/15 = 0.8.
To identify the location of point A' in the second right triangle A'B'C, we use this ratio.
The hypotenuse of triangle A'B'C is given as 0.8.
Since the ratio of the side opposite angle A to the hypotenuse of triangle ABC is 0.8, we can conclude that the side opposite angle A' in triangle A'B'C is 0.8 times the hypotenuse of triangle A'B'C.
Therefore, the length of the side opposite angle A' in triangle A'B'C is 0.8 * 18 = 14.4.
So the side opposite angle A' in triangle A'B'C has a length of 14.4.
Hence, the location of point A' in the second right triangle is on the side with length 14.4.