Question

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

Answer 1

Side opposite ∠C in ABC is AB = 8 and the hypotenuse is AC = 17, so the ratio is 8/17.
In A′B′C′ the hypotenuse is 34, so the side opposite C′ is (8/17)·34 = 16.

The length is 16 units.