190 likes | 380 Views
Chapter 6 – Trigonometric Functions: Right Triangle Approach. Section 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.
E N D
Chapter 6 – Trigonometric Functions: Right Triangle Approach Section 6.6 Law of Cosines 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.
Solving Using SAS Solve the triangles shown below.
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 N75E at 350 mph. How far apart will the airplanes be after two hours?
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. 6.6 - Law of Cosines