Demana, Waits, Foley, Kennedy 5.6 The Law of Cosines

What you’ll learn about Deriving the Law of Cosines Solving Triangles (SAS, SSS) Triangle Area and Heron’s Formula Applications … and why The Law of Cosines is an important extension of the Pythagorean theorem, with many applications.

Law of Cosines Pythag thrm-ish Angle & Side opp are at the ends

Example: Solving a Triangle (SAS)

Solution

Solution

Area of a Triangle Find the area of a triangle with sides 10, 12, 14.

Solution Find the area of a triangle with sides 10, 12, 14.

The figure shown is three mutually tangent circles, with a triangle whose vertices are at the midpoint of each circle. The radii of circles A, B and C are 6, 8 and 12. What is the area of the shaded region?

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