Question
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 sentences ( in a 6th grader’s response), describe how to find the ratio of the side opposite LA to the hypotenuse of triangle
ABC. Then use this ratio to identify the location of point A' in the second right triangle.
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 sentences ( in a 6th grader’s response), describe how to find the ratio of the side opposite LA to the hypotenuse of triangle
ABC. Then use this ratio to identify the location of point A' in the second right triangle.
Answers
GPT-4o mini
To find the ratio of the side opposite angle A to the hypotenuse in triangle ABC, we first need to identify the lengths of the sides. In triangle ABC, the side opposite angle A is AB, which is 6, and the hypotenuse CA is 10. So, the ratio is 6 divided by 10, which is the same as 3 divided by 5.
Now, for triangle A'B'C', we can use that same ratio of 3 to 5 to find the length of the side opposite angle A' (which is A'B') compared to the hypotenuse A'C'. Since A'C' is 32, we can set up the equation: A'B'/32 = 3/5. This means A'B' is 32 times 3 divided by 5, which gives us 19.2, so point A' is located 19.2 units from point B'.
Now, for triangle A'B'C', we can use that same ratio of 3 to 5 to find the length of the side opposite angle A' (which is A'B') compared to the hypotenuse A'C'. Since A'C' is 32, we can set up the equation: A'B'/32 = 3/5. This means A'B' is 32 times 3 divided by 5, which gives us 19.2, so point A' is located 19.2 units from point B'.