{"id":84631,"date":"2022-06-01T16:39:17","date_gmt":"2022-06-01T11:09:17","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=84631"},"modified":"2022-05-10T14:19:41","modified_gmt":"2022-05-10T08:49:41","slug":"eureka-math-grade-8-module-3-lesson-13","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-8-module-3-lesson-13\/","title":{"rendered":"Eureka Math Grade 8 Module 3 Lesson 13 Answer Key"},"content":{"rendered":"<h2>Engage NY Eureka Math 8th Grade Module 3 Lesson 13 Answer Key<\/h2>\n<h3>Eureka Math Grade 8 Module 3 Lesson 13 Exercise Answer Key<\/h3>\n<p>Exercises<br \/>\nUse the Pythagorean theorem to determine the unknown length of the right triangle.<\/p>\n<p>Exercise 1.<br \/>\nDetermine the length of side c in each of the triangles below.<\/p>\n<p>a. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-84643\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Eureka-Math-Grade-8-Module-3-Lesson-13-Exercise-Answer-Key-1.png\" alt=\"Eureka Math Grade 8 Module 3 Lesson 13 Exercise Answer Key 1\" width=\"224\" height=\"119\" \/><br \/>\nAnswer:<br \/>\n5<sup>2<\/sup>+12<sup>2<\/sup>=c<sup>2<\/sup><br \/>\n25+144=c<sup>2<\/sup><br \/>\n169=c<sup>2<\/sup><br \/>\n13=c<\/p>\n<p>b. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-84644\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Eureka-Math-Grade-8-Module-3-Lesson-13-Exercise-Answer-Key-2.png\" alt=\"Eureka Math Grade 8 Module 3 Lesson 13 Exercise Answer Key 2\" width=\"225\" height=\"133\" \/><br \/>\nAnswer:<br \/>\n0.5<sup>2<\/sup>+1.2<sup>2<\/sup>=c<sup>2<\/sup><br \/>\n0.25+1.44=c<sup>2<\/sup><br \/>\n1.69=c<sup>2<\/sup><br \/>\n1.3=c<\/p>\n<p>Exercise 2.<br \/>\nDetermine the length of side b in each of the triangles below.<br \/>\na. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-84645\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Eureka-Math-Grade-8-Module-3-Lesson-13-Exercise-Answer-Key-3.png\" alt=\"Eureka Math Grade 8 Module 3 Lesson 13 Exercise Answer Key 3\" width=\"170\" height=\"246\" \/><br \/>\nAnswer:<br \/>\n4<sup>2<\/sup>+b<sup>2<\/sup>=5<sup>2<\/sup><br \/>\n16+b<sup>2<\/sup>=25<br \/>\n16-16+b<sup>2<\/sup>=25-16<br \/>\nb<sup>2<\/sup>=9<br \/>\nb=3<\/p>\n<p>b. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-84646\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Eureka-Math-Grade-8-Module-3-Lesson-13-Exercise-Answer-Key-4.png\" alt=\"Eureka Math Grade 8 Module 3 Lesson 13 Exercise Answer Key 4\" width=\"228\" height=\"137\" \/><br \/>\nAnswer:<br \/>\n0.4<sup>2<\/sup>+b<sup>2<\/sup>=0.5<sup>2<\/sup><br \/>\n0.16+b<sup>2<\/sup>=0.25<br \/>\n0.16-0.16+b<sup>2<\/sup>=0.25-0.16<br \/>\nb<sup>2<\/sup>=0.09<br \/>\nb=0.3<\/p>\n<p>Exercise 3.<br \/>\nDetermine the length of \\(\\overline{Q S}\\). (Hint: Use the Pythagorean theorem twice.)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-84647\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Eureka-Math-Grade-8-Module-3-Lesson-13-Exercise-Answer-Key-5.png\" alt=\"Eureka Math Grade 8 Module 3 Lesson 13 Exercise Answer Key 5\" width=\"390\" height=\"167\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Eureka-Math-Grade-8-Module-3-Lesson-13-Exercise-Answer-Key-5.png 390w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Eureka-Math-Grade-8-Module-3-Lesson-13-Exercise-Answer-Key-5-300x128.png 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><br \/>\nAnswer:<br \/>\n15<sup>2<\/sup>+|QT|<sup>2<\/sup>=17<sup>2<\/sup><br \/>\n225+|QT|<sup>2<\/sup>=289<br \/>\n225-225+|QT|<sup>2<\/sup>=289-225<br \/>\n|QT|<sup>2<\/sup>=64<br \/>\n|QT| = 8<\/p>\n<p>15<sup>2<\/sup>+|TS|<sup>2<\/sup>=25<sup>2<\/sup><br \/>\n225+|TS|<sup>2<\/sup>=625<br \/>\n225-225+|TS|<sup>2<\/sup>=625-225<br \/>\n|TS|<sup>2<\/sup>=400<br \/>\n|TS|=20<br \/>\nSince |QT|+|TS|=|QS|, then the length of side \\(\\overline{Q S}\\) is 8+20, which is 28.<\/p>\n<h3>Eureka Math Grade 8 Module 3 Lesson 13 Exit Ticket Answer Key<\/h3>\n<p>Determine the length of side \\(\\overline{B D}\\) in the triangle below.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-84648\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Eureka-Math-Grade-8-Module-3-Lesson-13-Exit-Ticket-Answer-Key-6.png\" alt=\"Eureka Math Grade 8 Module 3 Lesson 13 Exit Ticket Answer Key 6\" width=\"370\" height=\"226\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Eureka-Math-Grade-8-Module-3-Lesson-13-Exit-Ticket-Answer-Key-6.png 370w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Eureka-Math-Grade-8-Module-3-Lesson-13-Exit-Ticket-Answer-Key-6-300x183.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><br \/>\nAnswer:<br \/>\nFirst, determine the length of side \\(\\overline{B C}\\).<br \/>\n12<sup>2<\/sup>+BC<sup>2<\/sup>=15<sup>2<\/sup><br \/>\n144+BC<sup>2<\/sup>=225<br \/>\nBC<sup>2<\/sup>=225-144<br \/>\nBC<sup>2<\/sup>=81<br \/>\nBC=9<\/p>\n<p>Then, determine the length of side \\(\\overline{C D}\\).<br \/>\n12<sup>2<\/sup>+CD<sup>2<\/sup>=13<sup>2<\/sup><br \/>\n144+CD<sup>2<\/sup>=169<br \/>\nCD<sup>2<\/sup>=169-144<br \/>\nCD<sup>2<\/sup>=25<br \/>\nCD=5<br \/>\nAdding the lengths of sides \\(\\overline{B C}\\) and \\(\\overline{C D}\\) determines the length of side \\(\\overline{B D}\\); therefore, 5+9=14. \\(\\overline{B D}\\) has a length of 14.<\/p>\n<h3>Eureka Math Grade 8 Module 3 Lesson 13 Problem Set Answer Key<\/h3>\n<p>Students practice using the Pythagorean theorem to find unknown lengths of right triangles.<\/p>\n<p>Use the Pythagorean theorem to determine the unknown length of the right triangle.<\/p>\n<p>Question 1.<br \/>\nDetermine the length of side c in each of the triangles below.<br \/>\na. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-84635\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Engage-NY-Math-Grade-8-Module-3-Lesson-13-Problem-Set-Answer-Key-20.png\" alt=\"Engage NY Math Grade 8 Module 3 Lesson 13 Problem Set Answer Key 20\" width=\"238\" height=\"118\" \/><br \/>\nAnswer:<br \/>\n6<sup>2<\/sup>+8<sup>2<\/sup>=c<sup>2<\/sup><br \/>\n36+64=c<sup>2<\/sup><br \/>\n100=c<sup>2<\/sup><br \/>\n10=c<\/p>\n<p>b. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-84636\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Engage-NY-Math-Grade-8-Module-3-Lesson-13-Problem-Set-Answer-Key-21.png\" alt=\"Engage NY Math Grade 8 Module 3 Lesson 13 Problem Set Answer Key 21\" width=\"223\" height=\"142\" \/><br \/>\nAnswer:<br \/>\n0.6<sup>2<\/sup>+0.8<sup>2<\/sup>=c<sup>2<\/sup><br \/>\n0.36+0.64=c<sup>2<\/sup><br \/>\n1=c<sup>2<\/sup><br \/>\n1=c<\/p>\n<p>Question 2.<br \/>\nDetermine the length of side a in each of the triangles below.<br \/>\na. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-84637\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Engage-NY-Math-Grade-8-Module-3-Lesson-13-Problem-Set-Answer-Key-22.png\" alt=\"Engage NY Math Grade 8 Module 3 Lesson 13 Problem Set Answer Key 22\" width=\"229\" height=\"132\" \/><br \/>\nAnswer:<br \/>\na<sup>2<\/sup>+8<sup>2<\/sup>=17<sup>2<\/sup><br \/>\na<sup>2<\/sup>+64=289<br \/>\na<sup>2<\/sup>+64-64=289-64<br \/>\na<sup>2<\/sup>=225<br \/>\na=15<\/p>\n<p>b. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-84638\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Engage-NY-Math-Grade-8-Module-3-Lesson-13-Problem-Set-Answer-Key-23.png\" alt=\"Engage NY Math Grade 8 Module 3 Lesson 13 Problem Set Answer Key 23\" width=\"133\" height=\"217\" \/><br \/>\nAnswer:<br \/>\na<sup>2<\/sup>+0.8<sup>2<\/sup>=1.7<sup>2<\/sup><br \/>\na<sup>2<\/sup>+0.64=2.89<br \/>\na<sup>2<\/sup>+0.64-0.64=2.89-0.64<br \/>\na<sup>2<\/sup>=2.25<br \/>\na=1.5<\/p>\n<p>Question 3.<br \/>\nDetermine the length of side b in each of the triangles below.<br \/>\na. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-84639\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Engage-NY-Math-Grade-8-Module-3-Lesson-13-Problem-Set-Answer-Key-24.png\" alt=\"Engage NY Math Grade 8 Module 3 Lesson 13 Problem Set Answer Key 24\" width=\"135\" height=\"217\" \/><br \/>\nAnswer:<br \/>\n20<sup>2<\/sup>+b<sup>2<\/sup>=25<sup>2<\/sup><br \/>\n400+b<sup>2<\/sup>=625<br \/>\n400-400+b<sup>2<\/sup>=625-400<br \/>\nb<sup>2<\/sup>=225<br \/>\nb=15<\/p>\n<p>b. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-84641\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Engage-NY-Math-Grade-8-Module-3-Lesson-13-Problem-Set-Answer-Key-25.png\" alt=\"Engage NY Math Grade 8 Module 3 Lesson 13 Problem Set Answer Key 25\" width=\"251\" height=\"145\" \/><br \/>\nAnswer:<br \/>\n2<sup>2<\/sup>+b<sup>2<\/sup>=2.5<sup>2<\/sup><br \/>\n4+b<sup>2<\/sup>=6.25<br \/>\n4-4+b<sup>2<\/sup>=6.25-4<br \/>\nb<sup>2<\/sup>=2.25<br \/>\nb=1.5<\/p>\n<p>Question 4.<br \/>\nDetermine the length of side a in each of the triangles below.<br \/>\na. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-84640\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Engage-NY-Math-Grade-8-Module-3-Lesson-13-Problem-Set-Answer-Key-25.1.png\" alt=\"Engage NY Math Grade 8 Module 3 Lesson 13 Problem Set Answer Key 25.1\" width=\"145\" height=\"212\" \/><br \/>\nAnswer:<br \/>\na<sup>2<\/sup>+12<sup>2<\/sup>=20<sup>2<\/sup><br \/>\na<sup>2<\/sup>+144=400<br \/>\na<sup>2<\/sup>+144-144=400-144<br \/>\na<sup>2<\/sup>=256<br \/>\na=16<\/p>\n<p>b. <img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-84642\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Engage-NY-Math-Grade-8-Module-3-Lesson-13-Problem-Set-Answer-Key-26.png\" alt=\"Engage NY Math Grade 8 Module 3 Lesson 13 Problem Set Answer Key 26\" width=\"215\" height=\"136\" \/><br \/>\nAnswer:<br \/>\na<sup>2<\/sup>+1.2<sup>2<\/sup>=2<sup>2<\/sup><br \/>\na<sup>2<\/sup>+1.44=4<br \/>\na<sup>2<\/sup>+1.44-1.44=4-1.44<br \/>\na<sup>2<\/sup>=2.56<br \/>\na=1.6<\/p>\n<p>Question 5.<br \/>\nWhat did you notice in each of the pairs of Problems 1\u20134? How might what you noticed be helpful in solving problems like these?<br \/>\nAnswer:<br \/>\nIn each pair of problems, the problems and solutions were similar. For example, in Problem 1, part (a) showed the sides of the triangle were 6, 8, and 10, and in part (b), they were 0.6, 0.8, and 1. The side lengths in part (b) were a tenth of the value of the lengths in part (a). The same could be said about parts (a) and (b) of Problems 2\u20134. This might be helpful for solving problems in the future. If I am given side lengths that are decimals, then I could multiply them by a factor of 10 to make whole numbers, which are easier to work with. Also, if I know common numbers that satisfy the Pythagorean theorem, like side lengths of 3, 4, and 5, then I recognize them more easily in their decimal forms, that is, 0.3, 0.4, and 0.5.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Engage NY Eureka Math 8th Grade Module 3 Lesson 13 Answer Key Eureka Math Grade 8 Module 3 Lesson 13 Exercise Answer Key Exercises Use the Pythagorean theorem to determine the unknown length of the right triangle. Exercise 1. Determine the length of side c in each of the triangles below. a. Answer: 52+122=c2 25+144=c2 &#8230; <a title=\"Eureka Math Grade 8 Module 3 Lesson 13 Answer Key\" class=\"read-more\" href=\"https:\/\/ccssanswers.com\/eureka-math-grade-8-module-3-lesson-13\/\" aria-label=\"More on Eureka Math Grade 8 Module 3 Lesson 13 Answer Key\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/84631"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=84631"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/84631\/revisions"}],"predecessor-version":[{"id":137271,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/84631\/revisions\/137271"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=84631"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=84631"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=84631"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}