{"id":"cb_question_bank:923d2d95-3040-457a-9715-ca51c9a73a8a","source_id":"cb_question_bank","source_item_id":"923d2d95-3040-457a-9715-ca51c9a73a8a","external_id":null,"ibn":"05777-DC","question_id":"6933b3d9","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.C.","skill":"Right triangles and trigonometry","difficulty":"H","score_band":7,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The figure presents right triangle R S T such that side R T is horizontal, vertex T is to the right of vertex R, and vertex S is above R T. Side R S is labeled 12. Side S T is labeled 5. Angle S is a right angle In triangle RST above, point W (not shown) lies on line segment R T . What is the value of cosine of angle R S W, minus sine of angle W S T ?","stimulus":"","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"standalone_image \"></div>\n      </div>\n","stem_html":"<p><img src=\"/api/assets/bf2be4d5c0f34c173ccf9e80df69336c58022a5b3175221a3e4b4a720910a969\" alt=\"The figure presents right triangle R S T such that side R T is horizontal, vertex T is to the right of vertex R, and vertex S is above R T. Side R S is labeled 12. Side S T is labeled 5. Angle S is a right angle\" width=\"118\" height=\"54\"></p><p class=\"stem_paragraph \">In triangle <span class=\"italic\">RST</span> above, point <span class=\"italic\">W</span> (not shown)<span class=\"formatted_line_break delivery_mode:Both \"></span> lies on <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f05ff04f0a86bfcddb221d3a63ebb11e40c3e173b8fc4f5b935dc54aac66866a\" alt=\"line segment R T\"></span></span>. What is the value of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9e52561fefce5341b54ad79198e48b54f5aad63a9bfd4a8b04d8168a0f17a7a9\" alt=\"cosine of angle R S W, minus sine of angle W S T\"></span></span> ?</p><p></p>\n","rationale_html":"<p>The correct answer is 0. Note that no matter where point <span class=\"italic\">W </span>is on <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f05ff04f0a86bfcddb221d3a63ebb11e40c3e173b8fc4f5b935dc54aac66866a\" alt=\"side R T\"></span>, the sum of the measures of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dd52b7ff45bdfbffdb5d7149850f2d364ddd501679e70e34c16ab84a001142f2\" alt=\"angle R S W\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3e9642160cdd5881e4de50b16d81330fa55a21c169bfc81bc5c048f6a680b7b7\" alt=\"angle W S T\"></span> is equal to the measure of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c60ffa4038a8de354fc15696ad73c110dd41605553593d711664a3d9e8622664\" alt=\"angle R S T\"></span>, which is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/64b4e01c27ff4e364299d314f9281e888bdd01137e9c7d6278e5c64f862aeb4c\" alt=\"90 degrees\"></span>. Thus, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dd52b7ff45bdfbffdb5d7149850f2d364ddd501679e70e34c16ab84a001142f2\" alt=\"angle R S W\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3e9642160cdd5881e4de50b16d81330fa55a21c169bfc81bc5c048f6a680b7b7\" alt=\"angle W S T\"></span> are complementary angles. Since the cosine of an angle is equal to the sine of its complementary angle, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2998756a942bf0a06c63c4cacdf27a492f52b8534fc645636d856e44085b1e07\" alt=\"the cosine of angle R S W, equals, the sine of angle W S T\"></span>. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/64bd15914ba3c9b13f81a0eec74fc72472c55637106408f876f7c250d6dcb58c\" alt=\"the cosine of angle R S W, minus, the sine of angle W S T, equals 0\"></span>.</p>\n","correct_answer":["0"],"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":[],"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}}