Starter MondayApril , 2015

a5

cA 51°

84°

𝒂sin 𝑨

=𝒃

sin𝑩=

𝒄sin𝑪

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

2. Find the measure of angle A.

Test Revisions• Overall goal: YOU learning new concepts and problem-

solving skills• Test goal: To see what you have learned, what you are still

learning, and to provide MULTIPLE opportunities to show mastery

1. Today, we will review the FIRST test answers together – take notes!

2. You will have until next class to study3. Next class, you will retake ONLY the questions you missed on

a NEW test4. Next class, you will turn in BOTH the NEW test AND the

FIRST test5. You need to retake questions if you have a 10 or less. A score

of 10/14 is 71.4 percent, which is a C-.

• If you haven’t taken the test yet:1. Take notes today2. Next class, you will take the NEW test

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.

Area of a Triangle

*Use this equation for area WHEN we know two (2) sides AND the angle between them (SAS).

ab

cA B

C

EITHER

OR

OR

Area of a Triangle

*Use this equation for area WHEN we know two (2) sides AND the angle between them (SAS).

a10

725° B

C

EITHER

OR

OR

Area of a Triangle

*Use this equation for area WHEN we know two (2) sides AND the angle between them (SAS).

231 m150 m

cA B

123°

EITHER

OR

OR

Law of Cosines

𝑐2=𝑎2+𝑏2−2∗𝑎∗𝑏∗ cos𝐶• 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

𝑐2=𝑎2+𝑏2−2∗𝑎∗𝑏∗ cos𝐶• 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 c

811

cA B

37°

Law of Cosines

𝑐2=𝑎2+𝑏2−2∗𝑎∗𝑏∗ cos𝐶• 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 C

86

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

• 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