How to find missing side of right triangle

{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T10:58:01+00:00","modifiedTime":"2021-07-09T15:02:42+00:00","timestamp":"2022-06-22T19:36:36+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"//dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"//dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Trigonometry","_links":{"self":"//dummies-api.dummies.com/v2/categories/33729"},"slug":"trigonometry","categoryId":33729}],"title":"How to Solve for a Missing Right Triangle Length","strippedTitle":"how to solve for a missing right triangle length","slug":"how-to-solve-for-a-missing-right-triangle-length","canonicalUrl":"","seo":{"metaDescription":"Use the Pythagorean theorem to figure out the length of one side of a right triangle if you have the lengths of the other two.","noIndex":0,"noFollow":0},"content":"The Pythagorean theorem states that <i>a</i>² + <i>b</i>² = <i>c</i>² in a right triangle where <i>c</i> is the longest side. You can use this equation to figure out the length of one side if you have the lengths of the other two. The figure shows two right triangles that are each missing one side's measure.\r\n\r\n<img src=\"//sg.cdnki.com/how-to-find-missing-side-of-right-triangle---aHR0cHM6Ly93d3cuZHVtbWllcy5jb20vd3AtY29udGVudC91cGxvYWRzLzQzOTY1NS5pbWFnZTAuanBn.webp\" alt=\"image0.jpg\" width=\"535\" height=\"338\" />\r\n\r\nIn the left triangle, the measure of the hypotenuse is missing. Use the Pythagorean theorem to solve for the missing length.\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Replace the variables in the theorem with the values of the known sides.</p>\r\n<p class=\"child-para\">48² + 14² = <i>c</i>²</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Square the measures and add them together.</p>\r\n<img src=\"//sg.cdnki.com/how-to-find-missing-side-of-right-triangle---aHR0cHM6Ly93d3cuZHVtbWllcy5jb20vd3AtY29udGVudC91cGxvYWRzLzQzOTY1Ni5pbWFnZTEuanBn.webp\" alt=\"image1.jpg\" width=\"175\" height=\"78\" />\r\n<img src=\"//sg.cdnki.com/how-to-find-missing-side-of-right-triangle---aHR0cHM6Ly93d3cuZHVtbWllcy5jb20vd3AtY29udGVudC91cGxvYWRzLzQzOTY1Ny5pbWFnZTIuanBn.webp\" alt=\"image2.jpg\" width=\"153\" height=\"76\" /></li>\r\n</ol>\r\nThe length of the missing side, <i>c</i>, which is the hypotenuse, is 50.\r\n\r\nThe triangle on the right is missing the bottom length, but you do have the length of the hypotenuse. It doesn't matter whether you call the missing length <i>a </i>or <i>b.</i>\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Replace the variables in the theorem with the values of the known sides.</p>\r\n<p class=\"child-para\">33² + <i>b</i>² = 183²</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Square the measures, and subtract 1,089 from each side.</p>\r\n<img src=\"//sg.cdnki.com/how-to-find-missing-side-of-right-triangle---aHR0cHM6Ly93d3cuZHVtbWllcy5jb20vd3AtY29udGVudC91cGxvYWRzLzQzOTY1OC5pbWFnZTMuanBn.webp\" alt=\"image3.jpg\" width=\"212\" height=\"78\" /></li>\r\n \t<li>\r\n<p class=\"first-para\">Find the square root of each side.</p>\r\n<img src=\"//sg.cdnki.com/how-to-find-missing-side-of-right-triangle---aHR0cHM6Ly93d3cuZHVtbWllcy5jb20vd3AtY29udGVudC91cGxvYWRzLzQzOTY1OS5pbWFnZTQuanBn.webp\" alt=\"image4.jpg\" width=\"166\" height=\"76\" /></li>\r\n</ol>\r\nThe length of the missing side is 180 units. That's not much shorter than the hypotenuse, but it still shows that the hypotenuse has the longest measure.","description":"The Pythagorean theorem states that <i>a</i>² + <i>b</i>² = <i>c</i>² in a right triangle where <i>c</i> is the longest side. You can use this equation to figure out the length of one side if you have the lengths of the other two. The figure shows two right triangles that are each missing one side's measure.\r\n\r\n<img src=\"//www.dummies.com/wp-content/uploads/439655.image0.jpg\" alt=\"image0.jpg\" width=\"535\" height=\"338\" />\r\n\r\nIn the left triangle, the measure of the hypotenuse is missing. Use the Pythagorean theorem to solve for the missing length.\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Replace the variables in the theorem with the values of the known sides.</p>\r\n<p class=\"child-para\">48² + 14² = <i>c</i>²</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Square the measures and add them together.</p>\r\n<img src=\"//www.dummies.com/wp-content/uploads/439656.image1.jpg\" alt=\"image1.jpg\" width=\"175\" height=\"78\" />\r\n<img src=\"//www.dummies.com/wp-content/uploads/439657.image2.jpg\" alt=\"image2.jpg\" width=\"153\" height=\"76\" /></li>\r\n</ol>\r\nThe length of the missing side, <i>c</i>, which is the hypotenuse, is 50.\r\n\r\nThe triangle on the right is missing the bottom length, but you do have the length of the hypotenuse. It doesn't matter whether you call the missing length <i>a </i>or <i>b.</i>\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Replace the variables in the theorem with the values of the known sides.</p>\r\n<p class=\"child-para\">33² + <i>b</i>² = 183²</p>\r\n</li>\r\n \t<li>\r\n<p class=\"first-para\">Square the measures, and subtract 1,089 from each side.</p>\r\n<img src=\"//www.dummies.com/wp-content/uploads/439658.image3.jpg\" alt=\"image3.jpg\" width=\"212\" height=\"78\" /></li>\r\n \t<li>\r\n<p class=\"first-para\">Find the square root of each side.</p>\r\n<img src=\"//www.dummies.com/wp-content/uploads/439659.image4.jpg\" alt=\"image4.jpg\" width=\"166\" height=\"76\" /></li>\r\n</ol>\r\nThe length of the missing side is 180 units. That's not much shorter than the hypotenuse, but it still shows that the hypotenuse has the longest measure.","blurb":"","authors":[{"authorId":8985,"name":"Mary Jane Sterling","slug":"mary-jane-sterling","description":" \t <p><b>Mary Jane Sterling</b> is the author of numerous <i>For Dummies</i> books. She has been teaching at Bradley University in Peoria, Illinois, for more than 25 years. ","_links":{"self":"//dummies-api.dummies.com/v2/authors/8985"}}],"primaryCategoryTaxonomy":{"categoryId":33729,"title":"Trigonometry","slug":"trigonometry","_links":{"self":"//dummies-api.dummies.com/v2/categories/33729"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":207754,"title":"Trigonometry For Dummies Cheat Sheet","slug":"trigonometry-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","trigonometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/207754"}},{"articleId":203563,"title":"How to Recognize Basic Trig Graphs","slug":"how-to-recognize-basic-trig-graphs","categoryList":["academics-the-arts","math","trigonometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/203563"}},{"articleId":203561,"title":"How to Create a Table of Trigonometry Functions","slug":"how-to-create-a-table-of-trigonometry-functions","categoryList":["academics-the-arts","math","trigonometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/203561"}},{"articleId":186910,"title":"Comparing Cosine and Sine Functions in a Graph","slug":"comparing-cosine-and-sine-functions-in-a-graph","categoryList":["academics-the-arts","math","trigonometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/186910"}},{"articleId":157287,"title":"Signs of Trigonometry Functions in Quadrants","slug":"signs-of-trigonometry-functions-in-quadrants","categoryList":["academics-the-arts","math","trigonometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/157287"}}],"fromCategory":[{"articleId":207754,"title":"Trigonometry For Dummies Cheat Sheet","slug":"trigonometry-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","trigonometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/207754"}},{"articleId":203563,"title":"How to Recognize Basic Trig Graphs","slug":"how-to-recognize-basic-trig-graphs","categoryList":["academics-the-arts","math","trigonometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/203563"}},{"articleId":203561,"title":"How to Create a Table of Trigonometry Functions","slug":"how-to-create-a-table-of-trigonometry-functions","categoryList":["academics-the-arts","math","trigonometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/203561"}},{"articleId":199411,"title":"Defining the Radian in Trigonometry","slug":"defining-the-radian-in-trigonometry","categoryList":["academics-the-arts","math","trigonometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/199411"}},{"articleId":187511,"title":"How to Use the Double-Angle Identity for Sine","slug":"how-to-use-the-double-angle-identity-for-sine","categoryList":["academics-the-arts","math","trigonometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/187511"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282640,"slug":"trigonometry-for-dummies-2nd-edition","isbn":"9781118827413","categoryList":["academics-the-arts","math","trigonometry"],"amazon":{"default":"//www.amazon.com/gp/product/1118827414/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"//www.amazon.ca/gp/product/1118827414/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"//www.tkqlhce.com/click-9208661-13710633?url=//www.chapters.indigo.ca/en-ca/books/product/1118827414-item.html&cjsku=978111945484","gb":"//www.amazon.co.uk/gp/product/1118827414/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"//www.amazon.de/gp/product/1118827414/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"//www.dummies.com/wp-content/uploads/trigonometry-for-dummies-2nd-edition-cover-9781118827413-203x255.jpg","width":203,"height":255},"title":"Trigonometry For Dummies","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"<p><b data-author-id=\"8985\">Mary Jane Sterling</b> is the author of <i>Algebra I For Dummies</i> and many other <i>For Dummies</i> titles. 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