Starter 15 9 θ. Test Revisions Overall goal: YOU learning new concepts and problem-solving skills...

Starter WednesdayApril , 2015

1. Use the Pythagorean Theorem () to find the third side of the triangle.

2. Find:

3. What makes this triangle special?

15

9

θ

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.

Law of Sines

𝒂sin 𝑨

=𝒃

sin𝑩=

𝒄sin𝑪

• 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

• Any two (2) fractions can be used from this equation to find the missing pieces

• It works for ANY triangle (not only right triangles)

ab

cA B

C

Law of Sines: Does it work?• 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

Find:85

962.2°

84.3°

33.5°

𝒂sin 𝑨

=¿

𝒃sin𝑩

=¿

𝒄sin𝑪

=¿

𝒂sin 𝑨

=𝒃

sin𝑩=

𝒄sin𝑪

Law of Sines: How to use it?• 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.

a7

cA

105°

35°

𝒂sin 𝑨

=𝒃

sin𝑩=

𝒄sin𝑪

Law of Sines: How to use it?• 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 B.

a4.7

5.5A

63°

B

𝒂sin 𝑨

=𝒃

sin𝑩=

𝒄sin𝑪

Law of Sines: Ambiguous Case

*This ONLY happens in the “Side-Side-Angle” case

𝒂sin 𝑨

=𝒃

sin𝑩=

𝒄sin𝑪

• 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 B.

a41

28A

39°

B

Law of Sines: Ambiguous Case

𝒂sin 𝑨

=𝒃

sin𝑩=

𝒄sin𝑪

• 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

Law of Sines: Ambiguous Case

𝒂sin 𝑨

=𝒃

sin𝑩=

𝒄sin𝑪

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