{"id":22,"date":"2018-06-25T17:27:35","date_gmt":"2018-06-25T21:27:35","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/?post_type=chapter&#038;p=22"},"modified":"2018-12-14T14:35:09","modified_gmt":"2018-12-14T19:35:09","slug":"triangles-three-sides-and-the-truth","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/chapter\/triangles-three-sides-and-the-truth\/","title":{"raw":"Triangles","rendered":"Triangles"},"content":{"raw":"<h1>Why triangles are important<\/h1>\r\nLearning about electrical theory necessitates the study of triangles. \u00a0More specifically: right triangles.\u00a0 Before we dig too much into the right triangle, let's go over two key points about triangles.\r\n<ul>\r\n \t<li>All triangles have three sides.\u00a0 (File this fact under the \"thank you Captain Obvious\" category.)<\/li>\r\n \t<li>All triangles contain 180 degrees.<\/li>\r\n<\/ul>\r\n[caption id=\"attachment_97\" align=\"aligncenter\" width=\"152\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Triangle-e1530128682322.png\"><img src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Triangle-e1530128682322-273x300.png\" alt=\"\" class=\"wp-image-97\" width=\"152\" height=\"167\" \/><\/a> <strong>Figure 9. Triangle<\/strong>[\/caption]\r\n<h1>Different triangles<\/h1>\r\nThe right triangle is the most common triangle that will be used in electrical theory.\u00a0 It is a good idea to have a basic understanding of other triangles as well.\u00a0 Here are some common triangles you will come across in trigonometry.\r\n\r\n<strong>Isosceles triangle.<\/strong>\u00a0 This triangle has two sides that are equal, and two angles that are equal.\r\n\r\n&nbsp;\r\n\r\n[caption id=\"attachment_106\" align=\"aligncenter\" width=\"134\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Isosceles-e1530128499899.png\"><img src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Isosceles-e1530128499899-181x300.png\" alt=\"\" class=\"wp-image-106\" width=\"134\" height=\"222\" \/><\/a> <strong>Figure 10. Isosceles\u00a0triangle<\/strong>[\/caption]\r\n\r\n<strong>Equilateral triangle.\u00a0<\/strong> All three sides of this triangle are equal, and all three of its angles are equal too.\r\n\r\n&nbsp;\r\n\r\n[caption id=\"attachment_105\" align=\"aligncenter\" width=\"157\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Equalateral-e1530128541337.png\"><img src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Equalateral-e1530128541337-279x300.png\" alt=\"\" class=\"wp-image-105\" width=\"157\" height=\"169\" \/><\/a> <strong>Figure 11. Equilateral triangle<\/strong>[\/caption]\r\n\r\n<strong>Similar triangles.<\/strong>\u00a0 These triangles each have different sized sides, but they share the same sized angles.\r\n\r\n[caption id=\"attachment_104\" align=\"aligncenter\" width=\"158\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Similartriangles-e1530128577293.png\"><img src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Similartriangles-e1530128577293-233x300.png\" alt=\"\" class=\"wp-image-104\" width=\"158\" height=\"203\" \/><\/a> <strong>Figure 12. Similar triangles<\/strong>[\/caption]\r\n<h1>So what about these right triangles you were talking about?<\/h1>\r\nA right triangle is a triangle that has one right angle (equal to 90 degrees).\u00a0 This means that the other two angles are complementary, that is, they must add to 90 degrees.\r\n\r\n[caption id=\"attachment_457\" align=\"aligncenter\" width=\"149\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Skitch-Image-3-e1544472313980-300x283.jpg\" alt=\"\" class=\"wp-image-457\" width=\"149\" height=\"141\" \/> <strong>Figure 13. Complementary angles.<\/strong>[\/caption]\r\n<h1>Ok, so what does a right triangle have to do with electrical?<\/h1>\r\nQuite a bit actually.\r\n\r\nIn the world of electrical theory, we will have to add up values.\u00a0 We call these units <strong>vectors<\/strong> (more on the concept of vectors in a later chapter). These <em>vectors<\/em> each head in a different direction.\u00a0 In fact, they are 90 degrees to each other. \u00a0When we add them,\u00a0the sum of these two vectors ends up being the point between the two sides.\r\n\r\n&nbsp;\r\n\r\n[caption id=\"attachment_102\" align=\"aligncenter\" width=\"160\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Vector90-e1530128646955.jpg\"><img src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Vector90-e1530128646955-300x270.jpg\" alt=\"\" class=\"wp-image-102\" width=\"160\" height=\"144\" \/><\/a> <strong>Figure 14. Vector triangle<\/strong>[\/caption]\r\n\r\nBecause they are not heading in the same direction (they are heading in directions that are 90 degrees to each other) we can't add them up normally.\u00a0 They have to be added <strong>vectorially<\/strong>.\u00a0 How do you do this?\u00a0 I'm glad you asked.\r\n\r\nUp next:\u00a0\u00a0<strong>Pythagoras' theorem<\/strong>","rendered":"<h1>Why triangles are important<\/h1>\n<p>Learning about electrical theory necessitates the study of triangles. \u00a0More specifically: right triangles.\u00a0 Before we dig too much into the right triangle, let&#8217;s go over two key points about triangles.<\/p>\n<ul>\n<li>All triangles have three sides.\u00a0 (File this fact under the &#8220;thank you Captain Obvious&#8221; category.)<\/li>\n<li>All triangles contain 180 degrees.<\/li>\n<\/ul>\n<figure id=\"attachment_97\" aria-describedby=\"caption-attachment-97\" style=\"width: 152px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Triangle-e1530128682322.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Triangle-e1530128682322-273x300.png\" alt=\"\" class=\"wp-image-97\" width=\"152\" height=\"167\" srcset=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Triangle-e1530128682322-273x300.png 273w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Triangle-e1530128682322-65x72.png 65w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Triangle-e1530128682322-225x248.png 225w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Triangle-e1530128682322-350x385.png 350w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Triangle-e1530128682322.png 578w\" sizes=\"auto, (max-width: 152px) 100vw, 152px\" \/><\/a><figcaption id=\"caption-attachment-97\" class=\"wp-caption-text\"><strong>Figure 9. Triangle<\/strong><\/figcaption><\/figure>\n<h1>Different triangles<\/h1>\n<p>The right triangle is the most common triangle that will be used in electrical theory.\u00a0 It is a good idea to have a basic understanding of other triangles as well.\u00a0 Here are some common triangles you will come across in trigonometry.<\/p>\n<p><strong>Isosceles triangle.<\/strong>\u00a0 This triangle has two sides that are equal, and two angles that are equal.<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_106\" aria-describedby=\"caption-attachment-106\" style=\"width: 134px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Isosceles-e1530128499899.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Isosceles-e1530128499899-181x300.png\" alt=\"\" class=\"wp-image-106\" width=\"134\" height=\"222\" srcset=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Isosceles-e1530128499899-181x300.png 181w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Isosceles-e1530128499899-65x108.png 65w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Isosceles-e1530128499899-225x373.png 225w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Isosceles-e1530128499899-350x581.png 350w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Isosceles-e1530128499899.png 358w\" sizes=\"auto, (max-width: 134px) 100vw, 134px\" \/><\/a><figcaption id=\"caption-attachment-106\" class=\"wp-caption-text\"><strong>Figure 10. Isosceles\u00a0triangle<\/strong><\/figcaption><\/figure>\n<p><strong>Equilateral triangle.\u00a0<\/strong> All three sides of this triangle are equal, and all three of its angles are equal too.<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_105\" aria-describedby=\"caption-attachment-105\" style=\"width: 157px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Equalateral-e1530128541337.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Equalateral-e1530128541337-279x300.png\" alt=\"\" class=\"wp-image-105\" width=\"157\" height=\"169\" srcset=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Equalateral-e1530128541337-279x300.png 279w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Equalateral-e1530128541337-65x70.png 65w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Equalateral-e1530128541337-225x242.png 225w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Equalateral-e1530128541337-350x376.png 350w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Equalateral-e1530128541337.png 583w\" sizes=\"auto, (max-width: 157px) 100vw, 157px\" \/><\/a><figcaption id=\"caption-attachment-105\" class=\"wp-caption-text\"><strong>Figure 11. Equilateral triangle<\/strong><\/figcaption><\/figure>\n<p><strong>Similar triangles.<\/strong>\u00a0 These triangles each have different sized sides, but they share the same sized angles.<\/p>\n<figure id=\"attachment_104\" aria-describedby=\"caption-attachment-104\" style=\"width: 158px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Similartriangles-e1530128577293.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Similartriangles-e1530128577293-233x300.png\" alt=\"\" class=\"wp-image-104\" width=\"158\" height=\"203\" srcset=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Similartriangles-e1530128577293-233x300.png 233w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Similartriangles-e1530128577293-65x84.png 65w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Similartriangles-e1530128577293-225x289.png 225w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Similartriangles-e1530128577293-350x450.png 350w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Similartriangles-e1530128577293.png 588w\" sizes=\"auto, (max-width: 158px) 100vw, 158px\" \/><\/a><figcaption id=\"caption-attachment-104\" class=\"wp-caption-text\"><strong>Figure 12. Similar triangles<\/strong><\/figcaption><\/figure>\n<h1>So what about these right triangles you were talking about?<\/h1>\n<p>A right triangle is a triangle that has one right angle (equal to 90 degrees).\u00a0 This means that the other two angles are complementary, that is, they must add to 90 degrees.<\/p>\n<figure id=\"attachment_457\" aria-describedby=\"caption-attachment-457\" style=\"width: 149px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Skitch-Image-3-e1544472313980-300x283.jpg\" alt=\"\" class=\"wp-image-457\" width=\"149\" height=\"141\" srcset=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Skitch-Image-3-e1544472313980-300x283.jpg 300w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Skitch-Image-3-e1544472313980-768x724.jpg 768w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Skitch-Image-3-e1544472313980-1024x966.jpg 1024w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Skitch-Image-3-e1544472313980-65x61.jpg 65w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Skitch-Image-3-e1544472313980-225x212.jpg 225w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Skitch-Image-3-e1544472313980-350x330.jpg 350w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Skitch-Image-3-e1544472313980.jpg 1425w\" sizes=\"auto, (max-width: 149px) 100vw, 149px\" \/><figcaption id=\"caption-attachment-457\" class=\"wp-caption-text\"><strong>Figure 13. Complementary angles.<\/strong><\/figcaption><\/figure>\n<h1>Ok, so what does a right triangle have to do with electrical?<\/h1>\n<p>Quite a bit actually.<\/p>\n<p>In the world of electrical theory, we will have to add up values.\u00a0 We call these units <strong>vectors<\/strong> (more on the concept of vectors in a later chapter). These <em>vectors<\/em> each head in a different direction.\u00a0 In fact, they are 90 degrees to each other. \u00a0When we add them,\u00a0the sum of these two vectors ends up being the point between the two sides.<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_102\" aria-describedby=\"caption-attachment-102\" style=\"width: 160px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Vector90-e1530128646955.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Vector90-e1530128646955-300x270.jpg\" alt=\"\" class=\"wp-image-102\" width=\"160\" height=\"144\" srcset=\"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Vector90-e1530128646955-300x270.jpg 300w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Vector90-e1530128646955-768x691.jpg 768w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Vector90-e1530128646955-1024x921.jpg 1024w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Vector90-e1530128646955-65x58.jpg 65w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Vector90-e1530128646955-225x202.jpg 225w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Vector90-e1530128646955-350x315.jpg 350w, https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-content\/uploads\/sites\/496\/2018\/06\/Vector90-e1530128646955.jpg 1271w\" sizes=\"auto, (max-width: 160px) 100vw, 160px\" \/><\/a><figcaption id=\"caption-attachment-102\" class=\"wp-caption-text\"><strong>Figure 14. Vector triangle<\/strong><\/figcaption><\/figure>\n<p>Because they are not heading in the same direction (they are heading in directions that are 90 degrees to each other) we can&#8217;t add them up normally.\u00a0 They have to be added <strong>vectorially<\/strong>.\u00a0 How do you do this?\u00a0 I&#8217;m glad you asked.<\/p>\n<p>Up next:\u00a0\u00a0<strong>Pythagoras&#8217; theorem<\/strong><\/p>\n","protected":false},"author":422,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-22","chapter","type-chapter","status-publish","hentry"],"part":46,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/chapters\/22","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/wp\/v2\/users\/422"}],"version-history":[{"count":25,"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/chapters\/22\/revisions"}],"predecessor-version":[{"id":539,"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/chapters\/22\/revisions\/539"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/parts\/46"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/chapters\/22\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/wp\/v2\/media?parent=22"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/chapter-type?post=22"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/wp\/v2\/contributor?post=22"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/wp\/v2\/license?post=22"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}