{"id":"cb_question_bank:c810519b-8252-4017-b449-5b895fc7dc04","source_id":"cb_question_bank","source_item_id":"c810519b-8252-4017-b449-5b895fc7dc04","external_id":null,"ibn":"028928-DC","question_id":"92eb236a","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.C.","skill":"Right triangles and trigonometry","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In a right triangle, the tangent of one of the two acute angles is the fraction with numerator the square root of 3, and denominator 3 . What is the tangent of the other acute angle?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">In a right triangle, the tangent of one of the two acute angles is <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/80074f9937062e38aed71faa7f4c407de0c0050c1884b60d8478b227d5d0483c\" alt=\"the fraction with numerator the square root of 3, and denominator 3\"></span></span>. What is the tangent of the other acute angle?</p>\n","rationale_html":"<p>Choice D is correct. The tangent of a nonright angle in a right triangle is defined as the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle. Using that definition for tangent, in a right triangle with legs that have lengths <span class=\"italic\">a</span> and <span class=\"italic\">b</span>, the tangent of one acute angle is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5cf6d5a41f6c0c6acf669bc86eac17f43cffafdb4d96ee9a04d1ef02f49619a7\" alt=\"the fraction a, over b\"></span> and the tangent for the other acute angle is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/31018689c1001ea9faa88b27427166e0b525a6a646726bd4ac5ebe6234d1c9f5\" alt=\"the fraction b over a\"></span>. It follows that the tangents of the acute angles in a right triangle are reciprocals of each other. Therefore, the tangent of the other acute angle in the given triangle is the reciprocal of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/80074f9937062e38aed71faa7f4c407de0c0050c1884b60d8478b227d5d0483c\" alt=\"the fraction, the square root of 3, end root, over 3, end fraction\"></span> or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0bd5d6013f03bcbfa241dbcfcf1fff4f41d2086b535f9edb5c01e57d54ddbf98\" alt=\"the fraction, 3 over the square root of 3, end fraction\"></span>.</p><p>Choice A is incorrect and may result from assuming that the tangent of the other acute angle is the negative of the tangent of the angle described. Choice B is incorrect and may result from assuming that the tangent of the other acute angle is the negative of the reciprocal of the tangent of the angle described. Choice C is incorrect and may result from interpreting the tangent of the other acute angle as equal to the tangent of the angle described.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.623000+00:00","source_updated_at":"2023-08-02T20:25:59.623000+00:00","options":[{"label":"A","content_html":"<span class=\"choice_cell align:right \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/346b3718f7d0d6efb41f49463b69fd37d5b56bd749bd4b1c6374cd18292024d7\" alt=\"the negative of the fraction with numerator the square root of 3, and denominator 3\"></span></span>\n          </span>\n","ord":0},{"label":"B","content_html":"<span class=\"choice_cell align:right \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/429e212634ba22f507be7817e2e02b3f7b8eb7781b3e440d32bf1c732ecded76\" alt=\"the negative of the fraction with numerator 3, and denominator the square root of 3\"></span></span>\n          </span>\n","ord":1},{"label":"C","content_html":"<span class=\"choice_cell align:right \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/80074f9937062e38aed71faa7f4c407de0c0050c1884b60d8478b227d5d0483c\" alt=\"the fraction with numerator the square root of 3, and denominator 3\"></span></span>\n          </span>\n","ord":2},{"label":"D","content_html":"<span class=\"choice_cell align:right \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0bd5d6013f03bcbfa241dbcfcf1fff4f41d2086b535f9edb5c01e57d54ddbf98\" alt=\"the fraction with numerator 3, and denominator the square root of 3\"></span></span>\n          </span>\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}}