Question

Right triangle ABC
has side lengths AB=6
, BC=63–√
, AND AC=12
. A second right triangle, A′B′C′
has side lengths of 83–√
, 8
, and 16
. Find the ratio of the side opposite ∠C
to the hypotenuse of triangle ABC
. Then use this ratio to identify the location of point C′
in the second right triangle.

(1 point)
Responses

The ratio of the opposite side to the hypotenuse is 12
, and point C′
is opposite the side that has length 83–√
.
The ratio of the opposite side to the hypotenuse is 1 half, and point cap c prime is opposite the side that has length 8 square root of 3.

The ratio of the opposite side to the hypotenuse is 21
, and point C′
is opposite the side that has length 8
.
The ratio of the opposite side to the hypotenuse is 2 over 1, and point cap c prime is opposite the side that has length 8.

The ratio of the opposite side to the hypotenuse is 12
, and point C′
is opposite the side that has length 8
.
The ratio of the opposite side to the hypotenuse is 1 half, and point cap c prime is opposite the side that has length 8.

The ratio of the opposite side to the hypotenuse is 3√2
, and point C′
is opposite the side that has length 83–√
.
The ratio of the opposite side to the hypotenuse is the fraction with numerator square root of 3 and denominator 2, and point cap c prime is opposite the side that has length 8 square root of 3.

Answer 1

Opposite side to ∠C is AB = 6 and hypotenuse is AC = 12, so the ratio is 6/12 = 1/2. In the second triangle the hypotenuse is 16, so the side giving the same ratio is 8 (8/16 = 1/2). Thus: the ratio is 1/2, and C′ is opposite the side of length 8.