{"id":3279,"date":"2022-01-02T13:27:26","date_gmt":"2022-01-02T13:27:26","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=3279"},"modified":"2022-03-04T13:23:09","modified_gmt":"2022-03-04T13:23:09","slug":"pythagorean-theorem-word-problems","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/pythagorean-theorem-word-problems\/","title":{"rendered":"Pythagorean Theorem Word Problems"},"content":{"rendered":"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text]\n<h2>Pythagorean Theorem On Word Problems<\/h2>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]Solve application problems that involve finding the side of a right triangle using the Pythagorean Theorem.[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]1. Substitute the given values in the <a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/pythagorean-theorem\">Pythagorean Theorem<\/a>.<br \/>\n<img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;a^{2}+b^{2}=c^{2}\" alt=\"\\fn_phv a^{2}+b^{2}=c^{2}\" align=\"absmiddle\" \/><br \/>\n2. Solve using <a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/5th-grade\/order-of-operations\">order of operations<\/a>.<\/p>\n[\/vc_column_text][vc_column_text el_class=”headingnew”]Example[\/vc_column_text][vc_column_text]<strong><span style=\"color: #16a085;\">The fire escape ladder from one balcony to the next is 5 meters long. The bottom of the ladder is 2.7 meters to the right of the top of the ladder. What is the vertical distance between the balconies? Round your answer to the nearest tenth.<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/applications-of-the-pythagorean-theorem\"><img loading=\"lazy\" class=\"alignnone \" style=\"margin-top: 10px;\" src=\"https:\/\/cdn.oryxlearning.com\/media_assets\/1605774020873.svg\" width=\"216\" height=\"311\" \/><\/a>[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]The length of the ladder is the hypotenuse, so 5 is substituted for c in the Pythagorean Theorem formula. 2.7 is one of the legs.<br \/>\n<img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;a^{2}+b^{2}=c^{2}\" alt=\"\\fn_phv a^{2}+b^{2}=c^{2}\" align=\"absmiddle\" \/><br \/>\n<img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;2.7^{2}+b^{2}=5^{2}\" alt=\"\\fn_phv 2.7^{2}+b^{2}=5^{2}\" align=\"absmiddle\" \/><br \/>\n<img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;7.29+b^{2}=25\" alt=\"\\fn_phv 7.29+b^{2}=25\" align=\"absmiddle\" \/><br \/>\n<img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;b^{2}=25-7.29\" alt=\"\\fn_phv b^{2}=25-7.29\" align=\"absmiddle\" \/><br \/>\n<img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;b^{2}=17.71\" alt=\"\\fn_phv b^{2}=17.71\" align=\"absmiddle\" \/><br \/>\n<img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;b=\\sqrt{17.71}\\approx&space;{\\color{Red}&space;4.2}\" alt=\"\\fn_phv b=\\sqrt{17.71}\\approx {\\color{Red} 4.2}\" align=\"absmiddle\" \/><br \/>\n<span style=\"color: #ff0000; margin-top: 10px;\">The vertical distance between the balconies is 4.2 meters.<\/span>[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice Pythagorean Theorem Word Problems[\/vc_column_text][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 1<\/h5>\n<p><strong><span style=\"color: #16a085;\">If a right triangle has legs that measure 3 and 4, what is the length of the hypotenuse?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/applications-of-the-pythagorean-theorem\"><img loading=\"lazy\" class=\"alignnone wp-image-3283 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/31-3.png\" alt=\"Pythagorean Theorem On Word Problems - Practice Problem 1\" width=\"216\" height=\"121\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/31-3.png 216w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/31-3-214x121.png 214w\" sizes=\"(max-width: 216px) 100vw, 216px\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/applications-of-the-pythagorean-theorem”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 2<\/h5>\n<p><strong><span style=\"color: #16a085;\">Find the length of the missing side. Round the answer to the nearest tenth if necessary.<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/applications-of-the-pythagorean-theorem\"><img loading=\"lazy\" class=\"alignnone wp-image-3285 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/32-1.png\" alt=\"Pythagorean Theorem On Word Problems - Practice Problem 2\" width=\"181\" height=\"251\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/applications-of-the-pythagorean-theorem”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 3<\/h5>\n<p><strong><span style=\"color: #16a085;\">To walk around the pond from point A to point B, you must walk 34 meters south and 41 meters east. If a bridge was build between points A and B across the pond, how many meters long would the bridge have to be? Round your answer to the nearest tenth.<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/applications-of-the-pythagorean-theorem\"><img loading=\"lazy\" class=\"alignnone wp-image-3288 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/33-8.png\" alt=\"Pythagorean Theorem On Word Problems - Practice Problem 3\" width=\"306\" height=\"189\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/33-8.png 306w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/33-8-300x185.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/applications-of-the-pythagorean-theorem”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 4<\/h5>\n<p><strong><span style=\"color: #16a085;\">When decorating a cake, the frosting is put into a cone-shaped bag. If the bag has a radius of 7cm and a slant height of 25 cm, what is the actual height of the bag to the nearest tenth of a cm?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/applications-of-the-pythagorean-theorem\"><img loading=\"lazy\" class=\"alignnone wp-image-3290 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/34-1.png\" alt=\"Pythagorean Theorem On Word Problems - Practice Problem 4\" width=\"247\" height=\"270\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/applications-of-the-pythagorean-theorem”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][\/vc_column][vc_column width=”1\/3″ css=”.vc_custom_1633369011398{margin-bottom: 50px !important;}”][vc_row_inner el_class=”stickynotee”][vc_column_inner][vc_single_image image=”2265″ img_size=”full” alignment=”center” css_animation=”fadeIn” css=”.vc_custom_1633509989314{border-radius: 10px !important;}” el_class=”stickypin”][vc_column_text]The <strong>hypotenuse<\/strong> is the side opposite of the right angle. It is the longest side.\u200b<\/p>\n<p>The <strong>legs<\/strong> are the two sides that form the right angle.\u200b<\/p>\n<p><strong>Pythagorean theorem<\/strong> – the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”boxxborder2″]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skill<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/pythagorean-theorem\"><span style=\"color: #ed5600;\">Pythagorean Theorem<\/span><\/a>[\/vc_column_text][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1635246999755{border-top-width: 7px !important;border-right-width: 7px !important;border-bottom-width: 7px !important;border-left-width: 7px !important;background-position: center !important;background-repeat: no-repeat !important;background-size: contain !important;border-left-color: #333399 !important;border-left-style: solid !important;border-right-color: #333399 !important;border-right-style: solid !important;border-top-color: #333399 !important;border-top-style: solid !important;border-bottom-color: #333399 !important;border-bottom-style: solid !important;border-radius: 35px !important;}”]<span style=\"color: #333399;\"><strong>Related Skill<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/distance-on-a-coordinate-plane\"><span style=\"color: #333399;\">Distance on a Coordinate Plane<\/span><\/a><br \/>\n[\/vc_column_text][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Grade 1″ color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F1st-grade%2Fmaths|title:Grade%201%20Math||”][vc_btn title=”Grade 2″ color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F2nd-grade%2Fmaths|title:Grade%202%20Math||”][vc_btn title=”Grade 3″ color=”violet” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F3rd-grade%2Fmaths|title:Grade%203%20Math||”][vc_btn title=”Grade 4″ color=”blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F4th-grade%2Fmaths|title:Grade%204%20Math||”][vc_btn title=”Grade 5″ color=”green” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F5th-grade%2Fmaths|title:Grade%205%20Math||”][vc_btn title=”Grade 6″ color=”info” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F6th-grade%2Fmaths|title:Grade%206%20Math||”][vc_btn title=”Grade 7″ color=”vista-blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F7th-grade%2Fmaths|title:Grade%207%20Math||”][vc_btn title=”Grade 8″ color=”mulled-wine” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F8th-grade%2Fmaths|title:Grade%208%20Math||”][\/vc_column_inner][\/vc_row_inner][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Trigonometry” color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Ftopics%2Fmaths%2Ftrigonometry|title:Trigonometry||”][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][\/vc_section]\n","protected":false},"excerpt":{"rendered":"<p>[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Pythagorean Theorem On Word Problems [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]Solve application problems that involve finding the side of a right triangle using the Pythagorean Theorem.[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]1. Substitute the given values in the Pythagorean Theorem. 2. […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.0 (Yoast SEO v17.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Pythagorean Theorem Word Problems | Oryx Learning<\/title>\n<meta name=\"description\" content=\"How To Solve Word Problems Using The Pythagorean Theorem? Find out if you can solve the words problem can be modelled using an right triangle. 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