Right triangle ABC has side lengths AB=8 , BC=15 , and AC=17 . A second right triangle, A′B′C′ , has side lengths of 34, 30, and 16. First, find the ratio of the side opposite ∠C to the hypotenuse of triangle ABC . Then, use this ratio to identify the side length opposite point C′ on the second right triangle.(1 point)

Question

The length of the side opposite C′ is units.

Answer 1

In triangle ABC, the side opposite angle C is AC.

Using the Pythagorean theorem, we can find the length of AC:

AC^2 = AB^2 + BC^2

AC^2 = 8^2 + 15^2

AC^2 = 64 + 225

AC^2 = 289

AC = √289

AC = 17

Therefore, the length of the side opposite angle C in triangle ABC is 17 units.

Now, let's use the ratio of the side opposite angle C in triangle ABC to the hypotenuse of triangle ABC to find the length of the side opposite point C' in triangle A'B'C'.

The ratio of the side opposite angle C in triangle ABC to the hypotenuse of triangle ABC is:

17/17 = 1/1

So, the side opposite point C' in triangle A'B'C' is:

1 * 34 = 34 units.

Therefore, the length of the side opposite point C' in triangle A'B'C' is 34 units.