Right triangle ABC has side lengths AB=7, BC=24, and AC=25. A second right triangle, A′B′C′, has side lengths of 50, 14, and 48. Find the ratio of the side opposite ∠A to the hypotenuse of triangle ABC. Use this ratio to identify the location of point A′ in the second right triangle.
Let's call the side opposite angle A in triangle ABC as x.
According to the Pythagorean theorem, we can write the following equation for triangle ABC:
x^2 + (24)^2 = (25)^2
x^2 + 576 = 625
x^2 = 625 - 576
x^2 = 49
x = 7
So, the side opposite angle A in triangle ABC is 7.
Now, let's find the ratio of the side opposite angle A to the hypotenuse of triangle ABC:
Ratio = Side opposite angle A / Hypotenuse = 7 / 25
We can use this ratio to identify the location of point A' in the second right triangle.
Given that the hypotenuse of the second right triangle is 50, we can calculate the side opposite angle A' using the ratio:
Side opposite angle A' = Ratio * Hypotenuse = (7/25) * 50
Side opposite angle A' = (7/25) * 50
Side opposite angle A' = 14
Therefore, point A' in the second right triangle is located opposite a side of length 14.