Question

Right triangle ABC
has side lengths AB=6
, BC=8
, and CA=10
. A second right triangle has corresponding vertices of A′
, B′
, and C′
, with side lengths of 32, 40, and 24. In 3–5 sentences, describe how to find the ratio of the side opposite ∠A
to the hypotenuse of triangle ABC
. Then use this ratio to identify the location of point A′
in the second right triangle.(4 points)

Answer 1

The side opposite ∠A in triangle ABC is BC = 8 and the hypotenuse is CA = 10, so the ratio is 8/10 = 4/5. The second triangle is similar (scale factor 4), and its hypotenuse is 40, so the side opposite A′ must be (4/5)·40 = 32. Therefore A′ is the vertex opposite the side of length 32 (i.e., corresponding to BC).