Solving a Right Triangle Given 2 Sides

Warm-Up

Solving a Right Triangle Given 2 Sides

=12

125

tan 1B 22.62

mA + mB = 90

mA + 22.62 =90

mA 67.38

CA SAT 9 STANDARDS:29.029.0 Find the area of a closed figure within a closed figure. 40.0. Identify the results of an algorithm.

Agenda:05/11/10Agenda:05/11/101.) Warm-up

2.) Questions:

WS Lesson 13.1 C

3.) Lesson 13.2: General Angels and Radian Measure

4.) Class/Homework

WS Lesson 13.2 A & B5.) Groups of 4 - STAY ON TASK!!

6.) Quiz: 13.1 – 13.2 Friday 5/14/10

Learning Objectives: (1) Angels in Standard Position (2) Arc Length & Areas of Sectors

Objective- To measure angles in standard position using degree and radian measure.

x

y

0

90

180

270

360initial side

terminal side

vertex

150

Draw an angle with the given measure in standard position. Tell which quadrant the terminal side lies.

x

y

30

240

Quadrant III

Draw an angle with the given measure in standard position. Tell which quadrant the terminal side lies.

x

y30

480

Quadrant II

Draw an angle with the given measure in standard position. Tell which quadrant the terminal side lies.

x

y

60

Quadrant IV

Draw an angle with the given measure in standard position. Tell which quadrant the terminal side lies.

x

y

500

Quadrant II

360 140

Radian Measure

Another way to measure angles.

x

y

r

1 radian

360 2  radians180  radians

r

Radian Measure

x

y

0

30

456090120

150

135

210

225240

270300

315

330

6

4

3

0

2

2

3

3

4

5

6

180

7

6

5

4

4

3

3

2

5

3

7

4

11

6

• To rewrite a degree measure in radians, multiply by

CONVERSIONS BETWEEN DEGREES AND RADIANS

л radians 180°

180°л radians

• To rewrite a radian measure in degrees, multiply by

1.  220

2.  80

 radians

180

11

9

11

9 radians

 radians

180

4

9

49

 radians

Converting Degrees to Radian Measure

Converting Radians to Degree Measure

1.  25

2.  67

180

 radians

36

72

180

 radians

154.3

• To rewrite a degree measure in radians, multiply by

CONVERSIONS BETWEEN DEGREES AND RADIANS

л radians 180°

180°л radians

• To rewrite a radian measure in degrees, multiply by

Arc Length and Area of a Sector

rarc lengths

centralangle

Arc Length: s r Area: A1

2r2

• The arc length s and

area A of a sector with

radius r and central

angle θ (measured

in radians) are as

follows:

Find the arc length and area of the sector.

10 cm

Arc Length: 103

s

60

60

 radians

180

3

10

3

Find the arc length and area of the sector.

10 cm

21Area: 10

2 3A

60

60

 radians

180

3

50

3