Acute Angles in a TriangleDate: 12/02/98 at 19:46:36 From: Kailey van der Spank Subject: Math - Grade 4 Triangles My question is: What is the greatest number of angles smaller than a right angle a triangle can have? I said 2 and got the answer wrong. Help. Date: 12/03/98 at 13:05:41 From: Doctor Peterson Subject: Re: Math - Grade 4 Triangles Hi, Kailey. I think you may have just read the question backward, because your answer would be right if the question were a little different. If one angle of a triangle is obtuse (bigger than a right angle), then the others both have to be acute (less than a right angle). You can either see that by just drawing an obtuse angle and seeing what happens if you make a second angle obtuse, or by knowing that the sum of the angles is always 180 degrees. This means that you have to have at least two acute angles. \ / \ / \ / \ / \ / \ / \ / \ / \ / +--------------+ But the question is not the least number of acute angles, but the greatest. If you draw a simple, ordinary triangle, it is likely to have three acute angles. For instance, an equilateral triangle will work: + / \ / \ / \ / \ / \ / \ / \ +---------------+ So a triangle can have either 2 or 3 acute angles, and the maximum is 3, not 2. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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