{"id":"cb_question_bank:440e37dd-7b7a-4bd9-b98f-4883e3b49699","source_id":"cb_question_bank","source_item_id":"440e37dd-7b7a-4bd9-b98f-4883e3b49699","external_id":null,"ibn":"06625-DC","question_id":"933fee1a","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.B.","skill":"Lines, angles, and triangles","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Triangles ABC and DEF are shown above. Which of the following is equal to the ratio B C over A, B ?","stimulus":"The figure presents two right triangles, A, B C and D E F. In triangle A, B C, side A, C is horizontal and side B C is drawn such that it is perpendicular to side A, C and point B, is above point C. Angle A, is labeled 32 degrees and the right angle symbol is indicated at angle C. In triangle D E F, side D F is horizontal, side E F is drawn such that it is perpendicular to side D F, and point E, is above point F. Angle D is labeled 58 degrees and the right angle symbol is indicated at angle F.","stimulus_html":"
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Triangles ABC and DEF are shown above. Which of the following is equal to the ratio \"B?

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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 \"side is the side opposite to the angle with measure 32° and AB is the hypotenuse in right triangle ABC, the ratio \"the is equal to \"the.

Alternate approach: The trigonometric ratios can be used to answer this question. In right triangle ABC, the ratio \"the. The angle E in triangle DEF has measure 32° because \"the. In triangle DEF, the ratio \"the. Therefore, \"the.

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

\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.630000+00:00","source_updated_at":"2023-08-02T20:25:59.630000+00:00","options":[{"label":"A","content_html":"\n \"D\n","ord":0},{"label":"B","content_html":"\n \"D\n","ord":1},{"label":"C","content_html":"\n \"D\n","ord":2},{"label":"D","content_html":"\n \"E\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}