1. Section 6.2
Law of Cosines

2. Objective By following instructions students will be able to:
Use the Law of Cosines to solve oblique triangles (SSS or SAS).
Use the Law of Cosines to model and solve real-life problems.
Use Heron’s Area Formula to find areas of triangles.

3. Law of Cosines
Sides
Angles A B C a b c

4. Example 1: Three Sides of a Triangle SSS
Find the three angles of the triangle in the figure below. C
a=8ft
c=14ft B A
b=19ft

5. Example 2: Two Sides and Included Angle -SAS
Find the remaining two angles and the side of the triangle in the figure below. A
15cm a C B
10cm

6. Example 3: Two sides and Included Angle - SAS
The pitcher’s mound on a softball field is 46 feet from home plate and the distance between the bases is 60 feet. (The pitcher’s mound is not halfway between home plate and second base). How far is the pitcher’s mound from first base?

7. Example 4: Two Sides and the Included Angle- SAS

8. Heron’s Area Formula
Given any triangle with sides a, b, and c, the area of the triangle is
Where

9. Example 5: Using Heron’s Area Formula
Find the area of the triangular region having sides of lengths a=43m, b=53m, and c=72m.

10. Revisit Objective Did we…
Use the Law of Cosines to solve oblique triangles (SSS or SAS)?
Use the Law of Cosines to model and solve real-life problems?
Use Heron’s Area Formula to find areas of triangles?

11. Homework
Pg 441 #1-31 ODD