{"id":72,"date":"2023-07-28T16:35:07","date_gmt":"2023-07-28T20:35:07","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/?post_type=chapter&p=72"},"modified":"2023-11-02T12:49:28","modified_gmt":"2023-11-02T16:49:28","slug":"origin-of-a-30-60-90-triangle","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/tradeskillsforsuccessnumeracy\/chapter\/origin-of-a-30-60-90-triangle\/","title":{"raw":"Origin of a 30-60-90 Triangle","rendered":"Origin of a 30-60-90 Triangle"},"content":{"raw":"Consider the Equilateral Triangle ABC where all sides have a measure of 2 units.\r\nSince all sides have the same measure, then the measure of each angle is 180\u00b0 divided by 3 = 60\u00b0\r\n\r\n\"\"\r\n\r\nWe then take ABC and cut it in two by drawing the angle bisector. From geometry, we know that in an equilateral triangle the angle bisector is also the altitude and the median. This really means that when we draw any one of these, angle A will be divided in 2 equal parts, BC will be divided in 2 equal parts, and AD will intersect BC at 90\u00b0.\r\n\r\nIn ABC, we can use The Theorem of Pythagoras to find the value of AD. Quickly, this means 2\u00b2 - 1\u00b2 = AD\u00b2 or 3 = AD\u00b2 giving \u00d63 = AD. Thus, in a 30-60-90 Triangle, the side opposite the right angle (hypotenuse) is 2, the side opposite the smallest angle is 1, and the side opposite the 60\u00b0 angle is \u00d63.\r\n\r\nWe also note that the hypotenuse is always double the smallest side in a 30-60-90\r\nTriangle.\r\n\r\n\"\"\r\n\r\n \r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n\"Why","rendered":"

Consider the Equilateral Triangle ABC where all sides have a measure of 2 units.
\nSince all sides have the same measure, then the measure of each angle is 180\u00b0 divided by 3 = 60\u00b0<\/p>\n

\"\"<\/p>\n

We then take ABC and cut it in two by drawing the angle bisector. From geometry, we know that in an equilateral triangle the angle bisector is also the altitude and the median. This really means that when we draw any one of these, angle A will be divided in 2 equal parts, BC will be divided in 2 equal parts, and AD will intersect BC at 90\u00b0.<\/p>\n

In ABC, we can use The Theorem of Pythagoras to find the value of AD. Quickly, this means 2\u00b2 – 1\u00b2 = AD\u00b2 or 3 = AD\u00b2 giving \u00d63 = AD. Thus, in a 30-60-90 Triangle, the side opposite the right angle (hypotenuse) is 2, the side opposite the smallest angle is 1, and the side opposite the 60\u00b0 angle is \u00d63.<\/p>\n

We also note that the hypotenuse is always double the smallest side in a 30-60-90
\nTriangle.<\/p>\n

\"\"<\/p>\n

 <\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

 <\/p>\n

 <\/p>\n

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