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 3–5 sentences, describe how to 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.
By dividing the lengths of the sides, the triangle ABC's side opposite ∆A to the hypotenuse is 3/5. By using this ratio to determine the second triangle's equivalent side point A′ is located across from the side of length 24.
The answer is very clear.
The answer is fully supported by details.
There may be a few errors in grammar, usage, or mechanics. Errors do not interfere with meaning.edit it to get 4/4 points
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 ∠A
to the hypotenuse of triangle ABC
. Then use this ratio to identify the location of point A′
in the second right triangle.
By dividing the lengths of the sides, the triangle ABC's side opposite ∆A to the hypotenuse is 3/5. By using this ratio to determine the second triangle's equivalent side point A′ is located across from the side of length 24.
The answer is very clear.
The answer is fully supported by details.
There may be a few errors in grammar, usage, or mechanics. Errors do not interfere with meaning.edit it to get 4/4 points
Answers
Answered by
GPT-4o mini
To find the ratio of the side opposite ∠A to the hypotenuse of triangle ABC, we first identify the lengths of the sides. In triangle ABC, the side opposite ∠A (which is side BC) measures 8, while the hypotenuse (side CA) measures 10. Thus, the ratio is calculated as 8/10, which simplifies to 4/5.
Using this ratio in the second triangle with side lengths 32, 40, and 24, we can identify the corresponding segment across from point A′. The hypotenuse of the second triangle is 40, and using the same 4/5 ratio, the length of the side opposite the angle corresponding to ∠A′ can be found by multiplying 40 by 4/5, which equals 32. Therefore, point A′ is located across from the side of length 32 in the second triangle.
Using this ratio in the second triangle with side lengths 32, 40, and 24, we can identify the corresponding segment across from point A′. The hypotenuse of the second triangle is 40, and using the same 4/5 ratio, the length of the side opposite the angle corresponding to ∠A′ can be found by multiplying 40 by 4/5, which equals 32. Therefore, point A′ is located across from the side of length 32 in the second triangle.