In right triangle ABC, the measure of angle B must be
58° because the sum of the measure of angle A, which is
32°, and the measure of angle B is
90°. Angle D in the right triangle DEF has measure
58°. Hence, triangles ABC and DEF are similar. Since BC is the side opposite to the angle with measure 32° and AB is the hypotenuse in right triangle ABC, the ratio
is equal to
Alternate approach: The trigonometric ratios can be used to answer this question. In right triangle ABC, the ratio
=sin(32°) The angle E in triangle DEF has measure 32° because m(∠D)+m(∠E)=90° In triangle DEF, the ratio
=sin(32°).Therefore,
= Choice A is incorrect because
is the inverse of the ratio
.Choice C is incorrect because
=, not
.Choice D is incorrect because
=,not