{"id":"cb_question_bank:ca8aad09-e2a4-410a-8c8a-6a1768acefd1","source_id":"cb_question_bank","source_item_id":"ca8aad09-e2a4-410a-8c8a-6a1768acefd1","external_id":null,"ibn":"09170-DC","question_id":"13d9a1c3","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":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the right triangle shown above, what is the length of line P Q ?","stimulus":"The figure presents triangle P Q R, where side P R is horizontal, and point Q is directly above point P. Angle P is a right angle. Angle R is labeled 30 degrees and side Q R is labeled 8.","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"standalone_image \">\n          <img src=\"/api/assets/06d150ea3b44fd8d97341cfdeae6d9b0df33a5c468fc22d252255157ee9020a9\" alt=\"The figure presents triangle P Q R, where side P R is horizontal, and point Q is directly above point P. Angle P is a right angle. Angle R is labeled 30 degrees and side Q R is labeled 8.\" width=\"99\" height=\"63\"></div>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">In the right triangle shown above, what is the length of&nbsp;<span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e50978c6a670f560303a6e7e11f390c62f4c7ef2316769548d9e94e6f4ba45be\" alt=\"line P Q\"></span></span>&nbsp;?</p>\n","rationale_html":"<p class=\"tcp-fd3ea050-58f4-4b16-a81d-baba01ecbcd1\">The correct answer is 4. Triangle <span class=\"italic\">PQR </span>has given angle measures of 30° and 90°, so the third angle must be 60° because the measures of the angles of a triangle sum to 180°. For any special right triangle with angles measuring 30°, 60°, and 90°, the length of the hypotenuse (the side opposite the right angle) is 2<span class=\"italic\">x</span>, where <span class=\"italic\">x</span> is the length of the side opposite the 30° angle. Segment <span class=\"italic\">PQ</span> is opposite the 30° angle. Therefore, 2(<span class=\"italic\">PQ</span>)<span class=\"italic\"></span> = 8 and <span class=\"italic\">PQ </span>= 4.</p>\n","correct_answer":["4"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.636000+00:00","source_updated_at":"2023-08-02T20:25:59.636000+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}}