1. 6.5 Law of Cosines

2. Law of Cosines – use if know 2 sides and the included angle or all 3 sides
The square of any side of a triangle is equal to the sum of the squares of the other 2 sides minus twice the product of those two sides times the cosine of the included angle.
If one of the angles of a triangle is a right triangle then cos C = 0 and the Law of Cosines becomes ___________________.

4. A B C
65º 5 8
Ex – Solve the triangle

5. EX – solve the triangle
The sides of a triangle are a = , b = , and c = Find the angles. A B C
63.14
76.536
39.701

6. Ex – solve the triangle Angle A = 46.3º, b = 8.6 and c = 14.4. 8.6 C A
46.3°
8.6

7. Heading & Bearing
In navigation a direction is often given as a bearing.

8. Ex – pg 515 #41
A pilot flies in a straight path for 1 hour and 30 minutes. She then makes a course correction, heading 10º to the right of her original course and flies 2 hours in the new direction. If she maintains a constant speed of 625 mph, how far is she from her starting position?

9. Heron’s formula
The area of a triangle ABC is given by:
Where

10. Pg 513 ex5
A businessman wishes to buy a triangular lot downtown. The lot’s three sides are 125, 280, and 315 ft. Find the area of the lot.

11. pg 513 #1-25 odd, all
Homework