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
To find the ratio of the side opposite ∠A to the hypotenuse of triangle ABC, we need to find the length of the side opposite ∠A in triangle ABC.
Using the Pythagorean Theorem, we can find the length of the side opposite ∠A in triangle ABC:
(AB)^2 + (BC)^2 = (AC)^2
9^2 + 12^2 = 15^2
81 + 144 = 225
225 = 225
Therefore, the side opposite ∠A in triangle ABC has a length of 9.
Now, let's use this ratio to identify the location of point A' in the second right triangle.
The ratio of the side opposite ∠A to the hypotenuse of triangle ABC is 9/15, which simplifies to 3/5.
In triangle A'B'C, the hypotenuse corresponds to side length 30 and therefore, the side opposite ∠A' is (3/5) * 30 = 18.
So, the location of point A' in the second right triangle is such that the side opposite ∠A' has a length of 18.