Triangles ABC and DEF are shown above. Which of the following is equal to the ratio

Choice B is correct. 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 (by angle-angle similarity). Since 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 . The angle E in triangle DEF has measure 32° because . In triangle DEF, the ratio . Therefore, .

Choice A is incorrect because is the reciprocal of the ratio . Choice C is incorrect because , not . Choice D is incorrect because , not .