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)
The length of the side opposite C′ is units.
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.