think back to geometry. write down the ways to prove that two triangles are congruent

Think back to geometry. Write down the ways to prove that two triangles are congruent.

Warm-Up: May 20, 2013

The Law of SinesSection 6.1

For a triangle with angle measures A, B, C and side lengths opposite those angles of a, b, c:

True for any triangle (acute, right, obtuse)

The Law of Sines

C

c

B

b

A

a

sinsinsin

c

C

b

B

a

A sinsinsin

Solving a triangle means finding all side lengths and angle measures

Use Law of Sines A+B+C=180˚ For examples, you-try’s and homework,

round side lengths and angle measures to 3 decimal places.

Law of Sines can be used to solve a triangle if 2 angles and 1 side are known (SAA or ASA) or two sides and an angle opposite one of them (SSA)

Solving a Triangle

1. Start by drawing a rough sketch of a triangle (not to scale)

2. Find the third angle measure (A+B+C=180˚)

3. Use Law of Sines twice to find the two missing side lengths

4. Draw a better version of your triangle (to scale)

5. Check that your longest side is across from biggest angle, shortest side is across from smallest angle

Solving a Triangle: SAA or ASA

Solve the triangle

Example 1: SAA

24

56

22

C

B

A

c

b

a

Solve the triangle

You-Try #1: SAA

82

64

14

C

B

A

c

b

a

Solve the triangle

Example 2: ASA

C

B

A

c

b

a

35

85

30

Solve the triangle

You-Try #2: ASA

5.22

40

12

C

B

A

c

b

a

Page 607 #1-13 Every Other Odd Page 608 #17-29 Every Other Odd Page 608 #33-45 Every Other Odd

Assignments

Find all angles θ in the interval [0, 2π) such that

Warm-Up: May 21, 2013

2

1sin

Homework Questions?

SSA: The Ambiguous Case Given two side lengths and an angle

opposite one of them, there could be 0, 1, or 2 triangles

Assume a, b, and A are given If , then there are no triangles If , then there is one right triangle If , then there are two

triangles If , then there is one triangle

The Law of Sines will give you the number of triangles

SSA: How Many Triangles?

Aba sinAba sin

baAb sinba

Solve the triangle

Example 3: SSA

C

B

A

c

b

a

20

40

30

Solve the triangle

Example 4: SSA

C

B

A

c

b

a

50

20

30

Solve the triangle

Example 5: SSA

C

B

A

c

b

a

150

30

10

Solve the triangle

You-Try #5: SSA

C

B

A

c

b

a

35

16

12

Page 607 #1-13 Every Other Odd Page 608 #17-29 Every Other Odd Page 608 #33-45 Every Other Odd

Assignments

Solve the triangle (hint: there are two solutions)

Warm-Up: May 22, 2013

C

B

A

c

b

a

28

13

8

Homework Questions?

An oblique triangle is one that does not contain a right angle

Area is one half the product of the length of two sides and the sine of the included angle

Area of an Oblique Triangle

CabArea

BacArea

AbcArea

sin2

1

sin2

1

sin2

1

Find the area of a triangle with the following measurements

Example 6: Area

22

50

20

A

feetc

feetb

Find the area of a triangle with the following measurements

You-Try #6: Area

125

5

8

B

yardsc

yardsa

Page 607 #1-13 Every Other Odd Page 608 #17-29 Every Other Odd Page 608 #33-45 Every Other Odd

Assignments