{"id":30,"date":"2018-06-25T17:40:14","date_gmt":"2018-06-25T21:40:14","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/?post_type=chapter&p=30"},"modified":"2018-12-14T14:55:27","modified_gmt":"2018-12-14T19:55:27","slug":"naming-the-sides-of-the-right-triangle","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/chapter\/naming-the-sides-of-the-right-triangle\/","title":{"raw":"Naming Right Triangle Sides","rendered":"Naming Right Triangle Sides"},"content":{"raw":"

What is this big fancy word, trigonometry?<\/h1>\r\nTrigonometry<\/strong> is the study of the relationship that exists between the sides and the angles of a triangle.<\/span>\r\n\r\nThat sounds complicated and scary.\r\n\r\nIt can be, but lucky for us we are only dealing with right triangles.\u00a0\u00a0This makes it very simple and almost fun.\u00a0 (Nerd alert!)\r\n

First steps<\/h1>\r\nWe have already learned how to determine the sides of a triangle using the Pythagoras' theorem. \u00a0Next up is using those sides to determine the angles.\u00a0\u00a0Lucky for us we know that in a right triangle we already have one 90-degree angle.\u00a0\u00a0We also know that if we can solve any of the other two angles, the third one is easy.\u00a0 (All triangles have 180 degrees.)\u00a0 Our next step is to name the sides of the triangle.\u00a0\u00a0The names of these sides are dependent on something called the designate angle<\/strong> or theta<\/strong>.\u00a0\u00a0Theta is an angle that you determine or is determined for you.\r\n\r\n[caption id=\"attachment_115\" align=\"aligncenter\" width=\"174\"]\"\"<\/a> Figure 16. Theta 1<\/strong>[\/caption]\r\n\r\n \r\n\r\n[caption id=\"attachment_116\" align=\"aligncenter\" width=\"161\"]\"\"<\/a> Figure 17. Theta 2<\/strong>[\/caption]\r\n\r\nNow once you have figured out which angle is your theta, we can get to business naming the sides.\r\n\r\nAdjacent<\/strong>.\u00a0 This is the side that sits\u00a0adjacent<\/em>\u00a0to the designate angle.\r\n\r\nOpposite<\/strong>.\u00a0 This is the side that sits\u00a0opposite<\/em>\u00a0to the designate angle.\r\n\r\nHypotenuse.<\/strong>\u00a0 This is the side that sits opposite<\/em> the 90-degree angle.\r\n\r\nThe hypotenuse is always the longest side of the triangle and doesn't care where the designate angle is. \u00a0It only cares that it is opposite the 90-degree angle.\r\n\r\n[caption id=\"attachment_117\" align=\"aligncenter\" width=\"165\"]\"\"<\/a> Figure 18. Hypotenuse <\/strong>[\/caption]\r\n\r\nAnd if we switch the designate angle, the names of the sides change as in Figure 19.\r\n\r\n \r\n\r\n[caption id=\"attachment_118\" align=\"aligncenter\" width=\"168\"]\"\"<\/a> Figure 19. Adjacent and Opposite sides switch places<\/strong>[\/caption]\r\n\r\nThe next chapter tells us what to do with these names.","rendered":"

What is this big fancy word, trigonometry?<\/h1>\n

Trigonometry<\/strong> is the study of the relationship that exists between the sides and the angles of a triangle.<\/span><\/p>\n

That sounds complicated and scary.<\/p>\n

It can be, but lucky for us we are only dealing with right triangles.\u00a0\u00a0This makes it very simple and almost fun.\u00a0 (Nerd alert!)<\/p>\n

First steps<\/h1>\n

We have already learned how to determine the sides of a triangle using the Pythagoras’ theorem. \u00a0Next up is using those sides to determine the angles.\u00a0\u00a0Lucky for us we know that in a right triangle we already have one 90-degree angle.\u00a0\u00a0We also know that if we can solve any of the other two angles, the third one is easy.\u00a0 (All triangles have 180 degrees.)\u00a0 Our next step is to name the sides of the triangle.\u00a0\u00a0The names of these sides are dependent on something called the designate angle<\/strong> or theta<\/strong>.\u00a0\u00a0Theta is an angle that you determine or is determined for you.<\/p>\n

\"\"<\/a>
Figure 16. Theta 1<\/strong><\/figcaption><\/figure>\n

 <\/p>\n

\"\"<\/a>
Figure 17. Theta 2<\/strong><\/figcaption><\/figure>\n

Now once you have figured out which angle is your theta, we can get to business naming the sides.<\/p>\n

Adjacent<\/strong>.\u00a0 This is the side that sits\u00a0adjacent<\/em>\u00a0to the designate angle.<\/p>\n

Opposite<\/strong>.\u00a0 This is the side that sits\u00a0opposite<\/em>\u00a0to the designate angle.<\/p>\n

Hypotenuse.<\/strong>\u00a0 This is the side that sits opposite<\/em> the 90-degree angle.<\/p>\n

The hypotenuse is always the longest side of the triangle and doesn’t care where the designate angle is. \u00a0It only cares that it is opposite the 90-degree angle.<\/p>\n

\"\"<\/a>
Figure 18. Hypotenuse <\/strong><\/figcaption><\/figure>\n

And if we switch the designate angle, the names of the sides change as in Figure 19.<\/p>\n

 <\/p>\n

\"\"<\/a>
Figure 19. Adjacent and Opposite sides switch places<\/strong><\/figcaption><\/figure>\n

The next chapter tells us what to do with these names.<\/p>\n","protected":false},"author":422,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-30","chapter","type-chapter","status-publish","hentry"],"part":46,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/chapters\/30","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":18,"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/chapters\/30\/revisions"}],"predecessor-version":[{"id":545,"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/chapters\/30\/revisions\/545"}],"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\/30\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/wp\/v2\/media?parent=30"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/pressbooks\/v2\/chapter-type?post=30"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/wp\/v2\/contributor?post=30"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/trigforelectricians\/wp-json\/wp\/v2\/license?post=30"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}