{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T10:58:01+00:00","modifiedTime":"2021-07-09T15:02:42+00:00","timestamp":"2022-09-14T18:18:23+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Trigonometry","_links":{"self":"https://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><sup>2</sup> + <i>b</i><sup>2</sup> = <i>c</i><sup>2</sup> 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=\"https://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\">48<sup>2</sup> + 14<sup>2</sup> = <i>c</i><sup>2</sup></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=\"https://www.dummies.com/wp-content/uploads/439656.image1.jpg\" alt=\"image1.jpg\" width=\"175\" height=\"78\" />\r\n<img src=\"https://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\">33<sup>2</sup> + <i>b</i><sup>2</sup> = 183<sup>2</sup></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=\"https://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=\"https://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.","description":"The Pythagorean theorem states that <i>a</i><sup>2</sup> + <i>b</i><sup>2</sup> = <i>c</i><sup>2</sup> 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=\"https://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\">48<sup>2</sup> + 14<sup>2</sup> = <i>c</i><sup>2</sup></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=\"https://www.dummies.com/wp-content/uploads/439656.image1.jpg\" alt=\"image1.jpg\" width=\"175\" height=\"78\" />\r\n<img src=\"https://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\">33<sup>2</sup> + <i>b</i><sup>2</sup> = 183<sup>2</sup></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=\"https://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=\"https://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":" <p><b>Mary Jane Sterling</b> is the author of <i>Algebra I For Dummies, Algebra Workbook For Dummies,</i> and many other <i>For Dummies</i> books. She taught at Bradley University in Peoria, Illinois for more than 30 years, teaching algebra, business calculus, geometry, and finite mathematics. 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How to Solve for a Missing Right Triangle Length

By: Mary Jane Sterling and

Updated: 07-09-2021

From The Book: Trigonometry For Dummies

Trigonometry For Dummies

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The Pythagorean theorem states that a² + b² = c² in a right triangle where c 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.

In the left triangle, the measure of the hypotenuse is missing. Use the Pythagorean theorem to solve for the missing length.

Replace the variables in the theorem with the values of the known sides.

48² + 14² = c²
Square the measures and add them together.

The length of the missing side, c, which is the hypotenuse, is 50.

The 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 a or b.

Replace the variables in the theorem with the values of the known sides.

33² + b² = 183²
Square the measures, and subtract 1,089 from each side.
Find the square root of each side.

The 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.

About This Article

This article is from the book:

Trigonometry For Dummies ,

About the book author:

Mary Jane Sterling is the author of Algebra I For Dummies and many other For Dummies titles. She has been teaching mathematics at Bradley University in Peoria, Illinois, for more than 30 years and has loved working with future business executives, physical therapists, teachers, and many others.

This article can be found in the category:

Trigonometry ,