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. if the side length is 18, is the hypotenuse 0.8 or 0.6

Question

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. if the side length is 18, is the hypotenuse 0.8 or 0.6

Answer 1

In right triangle ABC, we can see that side length AC is the hypotenuse. Therefore, the side opposite angle A is AB. So, the ratio of the side opposite angle A to the hypotenuse is 9/15 = 3/5.

In right triangle A'B'C, the side opposite angle A' is AB'. If we use the same ratio of 3/5 as triangle ABC, we can find the length of AB'.

Let's call the length of AB' as a. Using the ratio, we know that a/30 = 3/5. Cross-multiplying, we get 5a = 90, and solving for a, we find that a = 90/5 = 18.

So, the location of point A' in the second right triangle is on the side with length 18.

Now, in the second right triangle A'B'C, if the side length is 18, the ratio of the side opposite angle A' to the hypotenuse is 18/30 = 0.6.