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Lines, angles, and triangles SAT question
Math · Geometry and Trigonometry · Medium · Answer it here, explanation included.
Triangles ABC and DEF are shown above. Which of the following is equal to the ratio 
?
ExplanationShow
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 .
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