{"id":"cb_question_bank:0cb116a1-df55-4959-878c-cfbff26e1227","source_id":"cb_question_bank","source_item_id":"0cb116a1-df55-4959-878c-cfbff26e1227","external_id":"19da9e4a-267f-405a-bab5-768d4d5c4c29","ibn":null,"question_id":"33e29881","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.C.","skill":"Right triangles and trigonometry","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In right triangle upper R upper S upper T , the sum of the measures of angle upper R and angle upper S is 90 degrees. The value of sine left parenthesis upper R right parenthesis is StartFraction StartRoot 15 EndRoot Over 4 EndFraction . What is the value of cosine left parenthesis upper S right parenthesis ?","stimulus":"","stimulus_html":null,"stem_html":"<p>In right triangle <math alttext=\"upper R upper S upper T\"><mrow>\n\t<mi>R</mi>\n\t<mi>S</mi>\n\t<mi>T</mi>\n</mrow>\n</math>, the sum of the measures of angle <math alttext=\"upper R\"><mi>R</mi>\n</math> and angle <math alttext=\"upper S\"><mi>S</mi>\n</math> is <math alttext=\"90\"><mn>90</mn>\n</math> degrees. The value of <math alttext=\"sine left parenthesis upper R right parenthesis\"><mi>sin</mi><mfenced><mi>R</mi></mfenced></math> is <math alttext=\"StartFraction StartRoot 15 EndRoot Over 4 EndFraction\"><mrow>\n\t<mfrac>\n\t\t<msqrt>\n\t\t\t<mn>15</mn>\n\t\t</msqrt>\n\t\t<mn>4</mn>\n\t</mfrac>\n</mrow>\n</math>. What is the value of <math alttext=\"cosine left parenthesis upper S right parenthesis\"><mi>cos</mi><mfenced><mi>S</mi></mfenced></math>?</p>","rationale_html":"<p>Choice B is correct. The sine of any acute angle is equal to the cosine of its complement. It’s given that in right triangle <math alttext=\"upper R upper S upper T\"><mrow>\n\t<mi>R</mi>\n\t<mi>S</mi>\n\t<mi>T</mi>\n</mrow>\n</math>, the sum of the measures of angle <math alttext=\"upper R\"><mi>R</mi>\n</math> and angle <math alttext=\"upper S\"><mi>S</mi>\n</math> is <math alttext=\"90\"><mn>90</mn>\n</math> degrees. Therefore, angle <math alttext=\"upper R\"><mi>R</mi>\n</math> and angle <math alttext=\"upper S\"><mi>S</mi>\n</math> are complementary, and the value of <math alttext=\"sine upper R\"><mi>sin</mi><mi>R</mi></math> is equal to the value of <math alttext=\"cosine upper S\"><mi>cos</mi><mi>S</mi></math>. It's given that the value of <math alttext=\"sine upper R\"><mi>sin</mi><mi>R</mi></math> is <math alttext=\"StartFraction StartRoot 15 EndRoot Over 4 EndFraction\"><mfrac><msqrt><mn>15</mn></msqrt><mn>4</mn></mfrac></math>, so the value of&nbsp;<math alttext=\"cosine upper S\"><mi>cos</mi><mi>S</mi></math> is also <math alttext=\"StartFraction StartRoot 15 EndRoot Over 4 EndFraction\"><mfrac><msqrt><mn>15</mn></msqrt><mn>4</mn></mfrac></math>.</p>\n<p>Choice A is incorrect. This is the value of <math alttext=\"tangent upper S\"><mi>tan</mi><mi>S</mi></math>.</p>\n<p>Choice C is incorrect. This is the value of <math alttext=\"StartFraction 1 Over cosine upper S EndFraction\"><mfrac><mn>1</mn><mrow><mi>cos</mi><mi>S</mi></mrow></mfrac></math>.</p>\n<p>Choice D is incorrect. This is the value of <math alttext=\"StartFraction 1 Over tangent upper S EndFraction\"><mfrac><mn>1</mn><mrow><mi>tan</mi><mi>S</mi></mrow></mfrac></math>.</p>","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.840000+00:00","source_updated_at":"2023-08-02T20:25:59.840000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"StartFraction StartRoot 15 EndRoot Over 15 EndFraction\"><mrow>\n\t<mfrac>\n\t\t<msqrt>\n\t\t\t<mn>15</mn>\n\t\t</msqrt>\n\t\t<mn>15</mn>\n\t</mfrac>\n</mrow>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"StartFraction StartRoot 15 EndRoot Over 4 EndFraction\"><mrow>\n\t<mfrac>\n\t\t<msqrt>\n\t\t\t<mn>15</mn>\n\t\t</msqrt>\n\t\t<mn>4</mn>\n\t</mfrac>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"StartFraction 4 StartRoot 15 EndRoot Over 15 EndFraction\"><mrow>\n\t<mfrac>\n\t\t<mrow>\n\t\t\t<mn>4</mn>\n\t\t\t<msqrt>\n\t\t\t\t<mn>15</mn>\n\t\t\t</msqrt>\n\t\t</mrow>\n\t\t<mn>15</mn>\n\t</mfrac>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"StartRoot 15 EndRoot\"><msqrt>\n\t<mn>15</mn>\n</msqrt>\n</math></p>","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}}