# The law of cosines in finding the measure of an angle

Relating Concepts :To earn credit for this assignment, you must show work and explain your reasoning.

In chapter 7 we introduced two new formulas for the area of a triangle. We can now find the area A of the triangle using one of three formulas.

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1. Draw a triangle with vertices A(-5,-2), B(-3,1), and C(0,-4), and use the distance formula to find the lengths of the sides a, b, and c.

2. Then use the traditional formula ( A = 1/2 b*h) to find the area of the triangle ABC.

3. From chapter 7, find the area of triangle ABC; showing that the 3 formulas all lead to the same area.

a) First use the law of cosines to find the measure of an angle

b)Find the area of triangle ABC using Herons Formula.

c) Find the area of triangle ABC using the Law of Sines.

4)  Demonstrate how all 3 of the formulas are equivalent. = Relating Concepts

You should find that regardless of which formula you used, all three should give the same unit of measure for area.

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