{"id":"cb_question_bank:04a12a1c-1d2a-43ce-bc5f-609b428a4bb8","source_id":"cb_question_bank","source_item_id":"04a12a1c-1d2a-43ce-bc5f-609b428a4bb8","external_id":"62bc2dfe-0a0c-45ec-a764-c5f84ddbce67","ibn":null,"question_id":"bcb66188","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.C.","skill":"Right triangles and trigonometry","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Triangle upper F upper G upper H is similar to triangle upper J upper K upper L , where angle upper F corresponds to angle upper J and angles upper G and upper K are right angles. If sine left parenthesis upper F right parenthesis equals StartFraction 308 Over 317 EndFraction , what is the value of sine left parenthesis upper J right parenthesis ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Triangle <math alttext=\"upper F upper G upper H\"><mrow>\n\t<mi>F</mi>\n\t<mi>G</mi>\n\t<mi>H</mi>\n</mrow>\n</math> is similar to triangle <math alttext=\"upper J upper K upper L\"><mrow>\n\t<mi>J</mi>\n\t<mi>K</mi>\n\t<mi>L</mi>\n</mrow>\n</math>, where angle <math alttext=\"upper F\"><mi>F</mi>\n</math> corresponds to angle <math alttext=\"upper J\"><mi>J</mi>\n</math> and angles <math alttext=\"upper G\"><mi>G</mi>\n</math> and <math alttext=\"upper K\"><mi>K</mi>\n</math> are right angles. If <math alttext=\"sine left parenthesis upper F right parenthesis equals StartFraction 308 Over 317 EndFraction\"><mi>sin</mi><mfenced><mi>F</mi></mfenced><mo>=</mo><mrow><mfrac><mn>308</mn><mn>317</mn></mfrac></mrow></math>, what is the value of <math alttext=\"sine left parenthesis upper J right parenthesis\"><mi>sin</mi><mo>(</mo><mi>J</mi><mo>)</mo></math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice B is correct. If two triangles are similar, then their corresponding angles are congruent. It's given that right triangle <math alttext=\"upper F upper G upper H\"><mrow>\n\t<mi>F</mi>\n\t<mi>G</mi>\n\t<mi>H</mi>\n</mrow>\n</math> is similar to right triangle <math alttext=\"upper J upper K upper L\"><mrow>\n\t<mi>J</mi>\n\t<mi>K</mi>\n\t<mi>L</mi>\n</mrow>\n</math> and angle <math alttext=\"upper F\"><mi>F</mi>\n</math> corresponds to angle <math alttext=\"upper J\"><mi>J</mi>\n</math>. It follows that angle <math alttext=\"upper F\"><mi>F</mi>\n</math> is congruent to angle <math alttext=\"upper J\"><mi>J</mi>\n</math> and, therefore, the measure of angle <math alttext=\"upper F\"><mi>F</mi>\n</math> is equal to the measure of angle <math alttext=\"upper J\"><mi>J</mi>\n</math>. The sine ratios of angles of equal measure are equal. Since the measure of angle <math alttext=\"upper F\"><mi>F</mi>\n</math> is equal to the measure of angle <math alttext=\"upper J\"><mi>J</mi>\n</math>, <math alttext=\"sine left parenthesis upper F right parenthesis equals sine left parenthesis upper J right parenthesis\"><mi>sin</mi><mfenced><mi>F</mi></mfenced><mo>=</mo><mi>sin</mi><mfenced><mi>J</mi></mfenced></math>. It's given that <math alttext=\"sine left parenthesis upper F right parenthesis equals StartFraction 308 Over 317 EndFraction\"><mi>sin</mi><mfenced><mi>F</mi></mfenced><mo>=</mo><mfrac><mn>308</mn><mn>317</mn></mfrac></math>. Therefore, &nbsp;<math alttext=\"sine left parenthesis upper J right parenthesis\"><mi>sin</mi><mfenced><mi>J</mi></mfenced></math> is <math alttext=\"StartFraction 308 Over 317 EndFraction\"><mfrac><mn>308</mn><mn>317</mn></mfrac></math>.</p>\n<p>Choice A is incorrect. This is the value of <math alttext=\"cosine left parenthesis upper J right parenthesis\"><mi>cos</mi><mfenced><mi>J</mi></mfenced></math>, not the value of <math alttext=\"sine left parenthesis upper J right parenthesis\"><mi>sin</mi><mfenced><mi>J</mi></mfenced></math>.</p>\n<p>Choice C is incorrect. This is the reciprocal of the value of <math alttext=\"sine left parenthesis upper J right parenthesis\"><mi>sin</mi><mfenced><mi>J</mi></mfenced></math>, not the value of <math alttext=\"sine left parenthesis upper J right parenthesis\"><mi>sin</mi><mfenced><mi>J</mi></mfenced></math>.</p>\n<p>Choice D is incorrect. This is the reciprocal of the value of <math alttext=\"cosine left parenthesis upper J right parenthesis\"><mi>cos</mi><mfenced><mi>J</mi></mfenced></math>, not the value of <math alttext=\"sine left parenthesis upper J right parenthesis\"><mi>sin</mi><mfenced><mi>J</mi></mfenced></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 75 Over 317 EndFraction\"><mfrac>\n\t<mn>75</mn>\n\t<mn>317</mn>\n</mfrac>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"StartFraction 308 Over 317 EndFraction\"><mfrac>\n\t<mn>308</mn>\n\t<mn>317</mn>\n</mfrac>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"StartFraction 317 Over 308 EndFraction\"><mfrac>\n\t<mn>317</mn>\n\t<mn>308</mn>\n</mfrac>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"StartFraction 317 Over 75 EndFraction\"><mfrac>\n\t<mn>317</mn>\n\t<mn>75</mn>\n</mfrac>\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}}