sat-dog

90° Choice D is correct. It’s given that in triangle XYZ, the measure of angle X is , so triangle XYZ is a right triangle. It’s also given that point W lies on segment YZ, and segment WX is perpendicular to segment YZ. It follows that triangle WYX is a right triangle. Triangle WYX and triangle XYZ are right triangles with the same interior angle measure at point Y. It follows that triangle WYX and triangle XYZ are similar, where angles W, Y, and X in triangle WYX correspond to angles X, Y, and Z, respectively, in triangle XYZ. Since corresponding angles in similar triangles are congruent, their tangents have equal value. Thus, the tangent of angle Z is equal to the tangent of angle X in triangle WYX. The opposite side of angle X in triangle WYX is segment WY, and the adjacent side is segment WX. 572 It’s given that the length of segment WY is and the length of segment WX is 429 572 4 . It follows that the tangent of angle X in triangle WYX is 429, or 3. Therefore, tan 4 the value of Z is 3. 50 SAT PRACTICE TEST #11 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2 cos tan Choice A is incorrect. This is the value of Z, not Z. Choice B is incorrect. tan tan sin This is the value of Y, not Z. Choice C is incorrect. This is the value of Z, tan not Z.