To prove: The Law of cosine for a
Given data: In the
Method/Formula used:
Use co-ordinate geometry to derive the value of
Calculations:
The position of triangle ABC in x - y plane is shown in Fig. 1.
The vertex B of the triangle is taken as origin. AM is perpendicular to the side BC ,
In triangle
Therefore, coordinates of point A are
The side MC of triangle AMC is
Substitute
Now, from Pythagoras theorem in triangle AMC
Substitute b for AC ,
Similarly, by symmetry
Therefore, Law of cosine is,
Consider the law
Thus, in a right angle triangle ABC, in which
Hence, proved.
Chapter 9 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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