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.(1 point)
The ratio of the opposite side to the hypotenuse is 1.25, and point A′ is opposite the side that has length 24.
The ratio of the opposite side to the hypotenuse is 0.8, and point A′ is opposite the side that has length 18.
The ratio of the opposite side to the hypotenuse is 0.6, and point A′ is opposite the side that has length 18.
The ratio of the opposite side to the hypotenuse is 0.8, and point upper A prime is opposite the side that has length 24.
The ratio of the side opposite ∠A to the hypotenuse of triangle ABC is calculated by dividing the length of the side opposite ∠A (AB) by the hypotenuse (AC). So, the ratio is 9/15 = 0.6.
In triangle A′B′C′, if the ratio of the opposite side to the hypotenuse is 0.6, then we need to find the side opposite ∠A′ and the hypotenuse. The side opposite ∠A′ is given as 18. So, if we divide 18 by the ratio (0.6), we get the hypotenuse.
Hypotenuse = 18 / 0.6 = 30
Therefore, in the second right triangle A′B′C′, point A′ is opposite the side that has length 18, and the ratio of the side opposite ∠A′ to the hypotenuse is 18/30 = 0.6.
Therefore, the correct answer is: The ratio of the opposite side to the hypotenuse is 0.6, and point A′ is opposite the side that has length 18.