[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-267007-105":59,"doc-detail-267007-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","chapter-39-solutions-decoding-the-digital-sat","Chapter 39 Solutions - Decoding the Digital SAT","","This document provides solutions and explanations for trigonometry problems featured in Chapter 39, specifically tailored for the Digital SAT. It details step-by-step calculations for volume of a cone, tangent of an angle in a right triangle, and sine of an angle in a geometric construction. The solutions utilize the Pythagorean Theorem and trigonometric definitions to arrive at the correct answers, referencing common Pythagorean triples to expedite calculations. The document aims to guide students through complex problem-solving techniques relevant to standardized math assessments.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/chapter-39-solutions-decoding-the-digital-sat/267007/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/chapter-39-solutions-decoding-the-digital-sat/267007.png","ImageObject",300,407,{"name":92,"@type":93},"Jiven","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-03","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",24,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the formula for the volume of a cone?","Question",{"text":113,"@type":114},"The formula for the volume of a cone is V = (1/3) * pi * r^2 * h, where r is the radius of the base and h is the height of the cone.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How is the height of the cone calculated in the problem?",{"text":118,"@type":114},"The height of the cone is calculated using the Pythagorean Theorem or by recognizing the 6:8:10 Pythagorean triple, where the height is 8.",{"name":120,"@type":111,"acceptedAnswer":121},"What is the definition of tangent in a right triangle?",{"text":122,"@type":114},"The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},267007,1789413928,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":24},1099513958607,"https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399","2. In the cone shown above, the radius of the base is 6 and the slant height is 10. What is the approximate volume of the cone?  \nA) 62.8 B) 226.2 C) 301.5 D) 377  \nStep 1: Refer to the Reference Table for the formula for volume of a cone:  \n =  13   \nStep 2: Calculate the height of the cone using the Pythagorean Theorem or know your Pythagorean triple 6:8:10. (10 is the slant height or the hypotenuse, not the height; the height of this triangle is 8).  \nStep 3: Plug the numbers given into the equation.  \n =  13 (6 )  (8)   \n =  96   \n =  96  (3 . 14)  =  301.4  \nCorrect Answer: C  \nSolutions to Chapter 39: Trigonometry  \nB  \nA  \n1. In right triangle ABC above, the measure of side AB is 8 and the measure of side AC is 10. What is the value of tan A?  \nA)  \nB)  \nC)  \nD)  \nStep 1: Use the Pythagorean Theorem or know your Pythagorean Triple 6:8:10 to find that the length of BC = 6.  \nStep 2: Tangent =   \nTangent A =  =  Correct Answer: A  \n5 feet  \nxº xº  \n6 feet  \n2. Jaya sketches out the above diagram for the sail of a boat she is building. What is the value of sin x?  \nA)  \nB)  \nC)  \nD)  \n3  \n6  \n3  \nStep 1: First draw an altitude so that we can carve the triangle into two right triangles each with a base of 3. Step 2: Recognize this is a Pythagorean triple (3-4-5) or use the Pythagorean Theorem to find the height of 4.  \nStep 3: Sin =  Sin x = ~~ ~~  \nCorrect Answer: D","cbCaim5S1hWQrK1l","https://ap.wps.com/l/cbCaim5S1hWQrK1l","pdf",316685,"English","# Chapter 39 Solutions: Trigonometry\n## Question 1: Cone Volume\n## Question 2: Tangent in Right Triangle\n## Question 3: Sine in Geometric Diagram","[{\"question\":\"What is the formula for the volume of a cone?\",\"answer\":\"The formula for the volume of a cone is V = (1/3) * pi * r^2 * h, where r is the radius of the base and h is the height of the cone.\"},{\"question\":\"How is the height of the cone calculated in the problem?\",\"answer\":\"The height of the cone is calculated using the Pythagorean Theorem or by recognizing the 6:8:10 Pythagorean triple, where the height is 8.\"},{\"question\":\"What is the definition of tangent in a right triangle?\",\"answer\":\"The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side.\"}]","Chapter 39 Solutions - Decoding the Digital SAT | PDF"]