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

Question

Accepted Answer

Choice B is correct. In right triangle ABC , the measure of angle B must be 58&deg; because the sum of the measure of angle A , which is 32&deg;, and the measure of angle B is 90&deg;. Angle D in the right triangle DEF has measure 58&deg;. Hence, triangles ABC and DEF are similar (by angle-angle similarity). Since is the side opposite to the angle with measure 32&deg; 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&deg; 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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