Transcript CLASS 1 CHARACTERISTICS of FUNCTIONS, ALGEBRAICALLY

Chapter 6 – Trigonometric Functions:
Right Triangle Approach
6.6 - Law of Cosines
Law of Cosines

Like the Law of Sines, the Law of Cosines is also
used for oblique triangles.
Law of Cosines

We have two possible cases for the law of cosines.
 Case 1 – Two sides and the included angle (SAS)
 Case 2 – Three sides (SSS)
6.5 - Law of Sines
Definition

Law of Cosines works when we have SAS or SSS.
Hint for Solving SAS
Solving Using SAS
Solve the triangles shown below.
Hint for Solving SSS
Solving Using SSS
Solve the triangle ABC if a = 8, b = 19, and c = 14.
Application
Two airplanes leave an airport at the same time on
different runways. One flies directly north at
400 mph. The other flies on a bearing of N75E at
350 mph. How far apart will the airplanes be after
two hours?
Heron’s Formula
Using Heron’s Formula
Find the area of a triangle with a = 6 yards,
b = 16 yards, and c = 18 yards.
Example – pg. 481

Find the area of the shaded figure, rounded to two
decimals.
6.6 - Law of Cosines
Examples – pg. 481

Find the indicated side x or angle . (Use either the
Law of Sines or Law of Cosines, as appropriate.)
6.6 - Law of Cosines
More Examples – pg. 481
6.6 - Law of Cosines
More Examples – pg. 482
6.6 - Law of Cosines
More Examples – pg. 482
6.6 - Law of Cosines
More Examples – pg. 482
6.6 - Law of Cosines
More Examples – pg. 480

Solve triangle ABC.
13. a  3.0,
b  4.0,
C  53
14. b  60,
15. a  20,
c  30,
b  25,
A  70
c  22
16. a  10,
b  12,
c  16
6.6 - Law of Cosines