Starter TuesdayApril , 2015

a6

cA 49°

96°

𝒂sin 𝑨

=𝒃

sin𝑩=

𝒄sin𝑪

1. Use the Law of Sines to calculate side c of the triangle.

2. Now find the Area of a Triangle.EITHER OR OR

Objectives1. Use the Law of Sines to solve for the sides and angles of

ANY triangle.2. Use the Law of Cosines to solve for the sides and angles

of ANY triangle.3. Use sine to find the Area of a Triangle.

Law of Cosines• a, b, and c are sides• A, B, and C are angles

• Side a faces angle A; side b faces angle B; side c faces angle C

• Use Law of Cosines to find:• The third side of a

triangle when we know two sides and the angle between them; or

• The angles of a triangle when we know all three sides 

ab

cA B

C

Law of Cosines• a, b, and c are sides• A, B, and C are angles

• Side a faces angle A; side b faces angle B; side c faces angle C

• Calculate side c811

cA B

37°

Law of Cosines• a, b, and c are sides• A, B, and C are angles

• Side a faces angle A; side b faces angle B; side c faces angle C

• Calculate side c129

cA B

96°

Law of Cosines• a, b, and c are sides• A, B, and C are angles

• Side a faces angle A; side b faces angle B; side c faces angle C

• Calculate angle C86

7A B

C

Law of Cosines• a, b, and c are sides• A, B, and C are angles

• Side a faces angle A; side b faces angle B; side c faces angle C

• Calculate angle C1512

19A B

C

Law of Cosines• a, b, and c are sides• A, B, and C are angles

• Side a faces angle A; side b faces angle B; side c faces angle C

• Use Law of Cosines to find:• The third side of a

triangle when we know two sides and the angle between them

• The angles of a triangle when we know all three sides 

ab

cA B

C