{"id":"cb_question_bank:23b79d46-3d44-4137-96b6-94374de3bffd","source_id":"cb_question_bank","source_item_id":"23b79d46-3d44-4137-96b6-94374de3bffd","external_id":"2a19ba5d-f615-44cf-bbf1-badb5fc9d6f7","ibn":null,"question_id":"94364a79","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.B.","skill":"Lines, angles, and triangles","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Two nearby trees are perpendicular to the ground, which is flat. One of these trees is 10 feet tall and has a shadow that is 5 feet long. At the same time, the shadow of the other tree is 2 feet long. How tall, in feet, is the other tree?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Two nearby trees are perpendicular to the ground, which is flat. One of these trees is <math alttext=\"10\"><mn>10</mn>\n</math> feet tall and has a shadow that is <math alttext=\"5\"><mn>5</mn>\n</math> feet long. At the same time, the shadow of the other tree is <math alttext=\"2\"><mn>2</mn>\n</math> feet long. How tall, in feet, is the other tree?</p>","rationale_html":"<p>Choice B is correct. Each tree and its shadow can be modeled using a right triangle, where the height of the tree and the length of its shadow are the legs of the triangle. At a given point in time, the right triangles formed by two nearby trees and their respective shadows will be similar. Therefore, if the height of the other tree is <math alttext=\"x\"><mi>x</mi>\n</math>, in feet, the value of <math alttext=\"x\"><mi>x</mi>\n</math> can be calculated by solving the proportional relationship <math alttext=\"StartFraction 10 feet tall Over 5 feet long EndFraction equals StartFraction x feet tall Over 2 feet long EndFraction\"><mfrac><mrow><mn>10</mn><mo>&nbsp;</mo><mtext>feet&nbsp;tall</mtext></mrow><mrow><mn>5</mn><mo>&nbsp;</mo><mtext>feet&nbsp;long</mtext></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>x</mi><mo>&nbsp;</mo><mtext>feet&nbsp;tall</mtext></mrow><mrow><mn>2</mn><mo>&nbsp;</mo><mtext>feet&nbsp;long</mtext></mrow></mfrac></math>. This equation is equivalent to<math alttext=\"StartFraction 10 Over 5 EndFraction equals StartFraction x Over 2 EndFraction\"><mfrac><mn>10</mn><mn>5</mn></mfrac><mo>=</mo><mfrac><mi>x</mi><mn>2</mn></mfrac></math>, or <math alttext=\"2 equals StartFraction x Over 2 EndFraction\"><mn>2</mn><mo>=</mo><mfrac><mi>x</mi><mn>2</mn></mfrac></math>. Multiplying each side of the equation <math alttext=\"2 equals StartFraction x Over 2 EndFraction\"><mn>2</mn><mo>=</mo><mfrac><mi>x</mi><mn>2</mn></mfrac></math> by <math alttext=\"2\"><mn>2</mn>\n</math> yields <math alttext=\"4 equals x\"><mn>4</mn><mo>=</mo><mi>x</mi></math>. Therefore, the other tree is&nbsp;<math alttext=\"4 feet\"><mn>4</mn><mo>&nbsp;</mo><mtext>feet</mtext></math> tall.</p>\n<p>Choice A is incorrect and may result from calculating the difference between the lengths of the shadows, rather than the height of the other tree.</p>\n<p>Choice C is incorrect and may result from calculating the difference between the height of the <math alttext=\"10\"><mn>10</mn>\n</math>-foot-tall tree and the length of the shadow of the other tree, rather than calculating the height of the other tree.</p>\n<p>Choice D is incorrect and may result from a conceptual or calculation error.</p>","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.837000+00:00","source_updated_at":"2023-08-02T20:25:59.837000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"3\"><mn>3</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"4\"><mn>4</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"8\"><mn>8</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"27\"><mn>27</mn>\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}}