Cosines of Three AnglesDate: 05/08/2003 at 22:02:14 From: Shannon Subject: Angles of triangles Show that the largest angle of the triangle whose sides are 4, 5, and 6 is exactly twice the size of the smallest angle. Date: 05/08/2003 at 22:54:00 From: Doctor Mitteldorf Subject: Re: Angles of triangles You can calculate the cosines of the three angles using the Law of Cosines. For example, the largest angle: 6^2 = 4^2 + 5^2 - 2(4)(5) cos(C) cos(C) = 1/8 Once you have the two cosines, you can test the statement that angle C is twice angle A by using the cosine formula for double an angle: cos(2A) = cos^2(A) - sin^2(A) = 2cos^2(A) - 1 - Doctor Mitteldorf, The Math Forum http://mathforum.org/dr.math/ |
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