Right triangle ABC has side lengths AB = 9BC = 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 angle A to the hypotenuse of triangle ABCThen 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 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 A' is opposite the side that has length 18 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 24

Question

Right triangle ABC has side lengths AB = 9BC = 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 angle A to the hypotenuse of triangle ABCThen 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 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 A' is opposite the side that has length 18 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 24

Answer 1

To find the ratio of the side opposite angle A to the hypotenuse of triangle ABC, we need to find the length of the side opposite angle A and the length of the hypotenuse.

Let's start with triangle ABC. We are given that AB = 9BC, so if we let BC = x, then AB = 9x. We are also given that AC = 15. Using the Pythagorean theorem, we can find the length of BC:

BC^2 + AB^2 = AC^2
x^2 + (9x)^2 = 15^2
x^2 + 81x^2 = 225
82x^2 = 225
x^2 = 225/82
x = sqrt(225/82)
x ≈ 1.048

Therefore, BC ≈ 1.048 and AB ≈ 9(1.048) ≈ 9.432.

The length of the hypotenuse, AC, is given as 15.

Now, let's move on to the second right triangle, A'B'C'. We are given that the ratio of the side opposite angle A' to the hypotenuse is 0.8, and point A' is opposite the side that has length 24.

Let the side opposite angle A' be x. The hypotenuse is 30. So we have the equation:

x/30 = 0.8

Multiplying both sides by 30, we get:

x = 0.8(30)
x = 24

Therefore, the side opposite angle A' is 24.

Comparing this with triangle ABC, we can see that the lengths of the side opposite angle A in triangle ABC and the side opposite angle A' in triangle A'B'C' are the same (approximately 9.432). Furthermore, the hypotenuse in triangle ABC is 15, while the hypotenuse in triangle A'B'C' is 30.

Therefore, the ratio of the side opposite angle A to the hypotenuse of triangle ABC is 9.432/15 = approximately 0.628.

Using this ratio, we can identify the location of point A' in the second right triangle. Since the ratio of the side opposite angle A' to the hypotenuse is 0.8, and point A' is opposite the side that has length 24, we can set up the following equation:

(24/hypotenuse) = 0.628

Solving for the hypotenuse, we get:

hypotenuse = 24/0.628
hypotenuse ≈ 38.218

Therefore, point A' is located opposite the side that has length approximately 38.218 in the second right triangle. The correct answer is not given in the options provided.