{"id":1626,"date":"2013-11-17T22:24:40","date_gmt":"2013-11-17T22:24:40","guid":{"rendered":"http:\/\/theglobalschool.net\/maths\/?page_id=1626"},"modified":"2015-11-26T22:51:30","modified_gmt":"2015-11-26T22:51:30","slug":"ptj","status":"publish","type":"page","link":"http:\/\/maths.crusoecollege.vic.edu.au\/ptj\/","title":{"rendered":"Pythagoras and Trigonometry &#8211; Level J"},"content":{"rendered":"<h2>Pythagoras&#8217; Theorem<\/h2>\n<h3>Using Pythagoras&#8217; Theorem to find diagonal lengths<\/h3>\n<p><iframe loading=\"lazy\" title=\"Level J: Mapping with Pythagoras\" src=\"https:\/\/player.vimeo.com\/video\/147059051?dnt=1&amp;app_id=122963\" width=\"580\" height=\"326\" frameborder=\"0\" allow=\"autoplay; fullscreen; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<h4>Follow-up activities<\/h4>\n<ul>\n<li><a href=\"http:\/\/tube.geogebra.org\/m\/2127627\"><img loading=\"lazy\" decoding=\"async\" class=\"alignright size-thumbnail wp-image-2844\" src=\"http:\/\/maths.crusoecollege.vic.edu.au\/wp-content\/uploads\/2013\/11\/pythag-150x150.png\" alt=\"pythag\" width=\"150\" height=\"150\" \/><\/a><a href=\"http:\/\/tube.geogebra.org\/m\/2127627\" target=\"_blank\">Interactive:\u00a0Pythagoras&#8217; Theorem<\/a>\u00a0states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Drag the corners to change the side lengths.<\/li>\n<\/ul>\n<h3>Proving Pythagoras&#8217; Theorem<\/h3>\n<p><iframe loading=\"lazy\" title=\"Proving Pythagoras&#039; Theorem\" src=\"https:\/\/player.vimeo.com\/video\/82360002?dnt=1&amp;app_id=122963\" width=\"580\" height=\"433\" frameborder=\"0\" allow=\"autoplay; fullscreen; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<h4>Instructions<\/h4>\n<p>How does Pythagoras&#8217; Theorem work?<\/p>\n<ol>\n<li>Redraw the diagram and label clearly.<\/li>\n<li>Annotate the diagram with all you know about the lengths, angles, shapes and areas on the diagram.<\/li>\n<li>Can you prove that c<sup>2<\/sup>\u00a0= a<sup>2<\/sup>\u00a0+ b<sup>2<\/sup>?<\/li>\n<\/ol>\n<h4>Required Materials<\/h4>\n<ul>\n<li><a href=\"http:\/\/maths.crusoecollege.vic.edu.au\/wp-content\/uploads\/2013\/11\/proof-of-the-pythagorean-theorem.pdf\">proof of the pythagorean theorem<\/a><\/li>\n<li><a href=\"http:\/\/maths.crusoecollege.vic.edu.au\/wp-content\/uploads\/2013\/11\/sample-proofs-of-the-pythagorean-theorem.pdf\">sample proofs of the pythagorean theorem<\/a><\/li>\n<\/ul>\n<h4>Extra Resources<\/h4>\n<ul>\n<li><a href=\"http:\/\/class.crusoecollege.vic.edu.au\/mod\/url\/view.php?id=1020\">References: Mathematics Assessment Project<\/a><\/li>\n<li><a href=\"http:\/\/class.crusoecollege.vic.edu.au\/mod\/url\/view.php?id=1034\">99 Pythagorean Proofs!<\/a><\/li>\n<\/ul>\n<h2>Trigonometry<\/h2>\n<h3>Triangle measurement<\/h3>\n<p><iframe loading=\"lazy\" title=\"Investigating Trigonometry\" src=\"https:\/\/player.vimeo.com\/video\/82360476?dnt=1&amp;app_id=122963\" width=\"580\" height=\"401\" frameborder=\"0\" allow=\"autoplay; fullscreen; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<h4>Instructions<\/h4>\n<p>Trigonometry literally means &#8220;triangle measurement&#8221;.<\/p>\n<ol>\n<li>Measure the sides of your group of eight\u00a0similar triangles\u00a0(different sizes but same shape). What makes them similar?<\/li>\n<li>Record your measurements in the table. Record the angle size of your triangles.<\/li>\n<li>Calculate the ratios of each pair of sides (three sides means three pairs). Do you notice a pattern?<\/li>\n<li>Calculate the mean (average) of the ratios. Share your results with the class and construct a graph of the ratios.<\/li>\n<li>Use a calculator to find the sine, cosine and tangent (sin, cos, tan) of your angle size. What do you notice?<\/li>\n<li>If the ratios for a certain angle size are always the same, we can use these relationships to find an unknown side or angle. Would you prefer to repeat this kind of triangle measurement or use a calculator?<\/li>\n<\/ol>\n<h4>Required Materials<\/h4>\n<ul>\n<li><a href=\"http:\/\/maths.crusoecollege.vic.edu.au\/wp-content\/uploads\/2013\/11\/triangles.pdf\">triangles<\/a><\/li>\n<li><a href=\"http:\/\/maths.crusoecollege.vic.edu.au\/wp-content\/uploads\/2013\/11\/results-table.pdf\">results table<\/a><\/li>\n<li><a href=\"http:\/\/maths.crusoecollege.vic.edu.au\/wp-content\/uploads\/2013\/11\/class-graph.pdf\">class graph<\/a><\/li>\n<\/ul>\n<h4>Follow-up activities<\/h4>\n<ul>\n<li><a href=\"http:\/\/tube.geogebra.org\/m\/2136147\"><img loading=\"lazy\" decoding=\"async\" class=\"alignright size-thumbnail wp-image-2843\" src=\"http:\/\/maths.crusoecollege.vic.edu.au\/wp-content\/uploads\/2013\/11\/trig-150x150.png\" alt=\"trig\" width=\"150\" height=\"150\" \/><\/a><a href=\"http:\/\/tube.geogebra.org\/m\/2136147\" target=\"_blank\">Interactive:\u00a0Trigonometric Ratios<\/a>\u00a0The three trigonometric ratios represented on a right-angled triangle. Drag the corners\u00a0to see how changing the scale and angle size changes the ratios.<\/li>\n<li>Skills practice:\u00a0<a href=\"http:\/\/maths.crusoecollege.vic.edu.au\/wp-content\/uploads\/2013\/11\/Using-the-Trig-Ratios.pdf\">Using the Trig Ratios<\/a><\/li>\n<\/ul>\n<h4>Extra Resources<\/h4>\n<ul>\n<li><a href=\"http:\/\/class.crusoecollege.vic.edu.au\/mod\/url\/view.php?id=1021\">Resources: NSW Department of Education<\/a><\/li>\n<\/ul>\n<h3>Use Trigonometry to calculate the size of things<\/h3>\n<p><iframe loading=\"lazy\" title=\"Use Trigonometry to calculate the size of things\" src=\"https:\/\/player.vimeo.com\/video\/82359355?dnt=1&amp;app_id=122963\" width=\"580\" height=\"401\" frameborder=\"0\" allow=\"autoplay; fullscreen; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p>Choose large objects around the school, measure sides and angles to calculate &#8216;unmeasurable&#8217; sides and angles (at least one of each).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pythagoras&#8217; Theorem Using Pythagoras&#8217; Theorem to find diagonal lengths Follow-up activities Interactive:\u00a0Pythagoras&#8217; Theorem\u00a0states that the square of the hypotenuse is equal to the sum of the squares of&hellip;<\/p>\n","protected":false},"author":4,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"_links":{"self":[{"href":"http:\/\/maths.crusoecollege.vic.edu.au\/wp-json\/wp\/v2\/pages\/1626"}],"collection":[{"href":"http:\/\/maths.crusoecollege.vic.edu.au\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/maths.crusoecollege.vic.edu.au\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/maths.crusoecollege.vic.edu.au\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"http:\/\/maths.crusoecollege.vic.edu.au\/wp-json\/wp\/v2\/comments?post=1626"}],"version-history":[{"count":2,"href":"http:\/\/maths.crusoecollege.vic.edu.au\/wp-json\/wp\/v2\/pages\/1626\/revisions"}],"predecessor-version":[{"id":2846,"href":"http:\/\/maths.crusoecollege.vic.edu.au\/wp-json\/wp\/v2\/pages\/1626\/revisions\/2846"}],"wp:attachment":[{"href":"http:\/\/maths.crusoecollege.vic.edu.au\/wp-json\/wp\/v2\/media?parent=1626"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}