Transcript Solving a Right Triangle Given 2 Sides Warm-Up

Warm-Up
Solving a Right Triangle Given 2 Sides
“Find all six parts.”
Solving a Right Triangle Given 2 Sides
=12
Math Joke
5
B  tan
 22.62
12
1
mA + mB = 90
mA + 22.62 =90
mA  67.38
Why do Mathematicians
NEVER go to the
beach?
Because they have
the sin & cos to get
the Tan!!
CA SAT 9 STANDARDS:
29.0 Find the area of a closed figure within a closed figure.
40.0. Identify the results of an algorithm.
Learning Objectives: (1) Angles in Standard Position (2) Arc
Length & Areas of Sectors
Agenda:05/9/12
1.) Warm-up
2.) Questions:
WS Lesson 13.1 A & B
3.) Lesson 13.2: General Angles and Radian Measure
4.) Class/Homework
TB pg. 780 – 781 #’s 25 – 76 ALL
5.) Groups of 4 - STAY ON TASK!!
6.) Quiz: Next Week
Objective- To measure angles in standard
position using degree and radian measure.
terminal
side
y
90
150
0
initial side 360x
180
vertex
270
Draw an angle with the given measure in standard
position. Tell which quadrant the terminal side lies.
240
y
x
Quadrant III
30
Draw an angle with the given measure in standard
position. Tell which quadrant the terminal side lies.
480
30
y
Quadrant II
x
Draw an angle with the given measure in standard
position. Tell which quadrant the terminal side lies.
60
y
x
Quadrant IV
Draw an angle with the given measure in standard
position. Tell which quadrant the terminal side lies.
500360  140
y
Quadrant II
x
Radian Measure
Another way to measure angles.
y
r
r
1 radian
x
360  2 radians
180   radians
Radian Measure

2

2
3
3
3 
90 60
120
4
4
45
135

5
30 6
6 150
 180
0 0
y
x
7 210
330 11
6
6
315
5 225
7
240
300
4 4
270
5 4
3
3
3
Copy This!
2
CONVERSIONS BETWEEN DEGREES AND RADIANS
• To rewrite a degree measure in radians, multiply by л radians
180°
• To rewrite a radian measure in degrees, multiply by
180°
л radians
Converting Degrees to Radian Measure
11
1. 220   radians   11 radians


9
 180 
9
4   radians  4
2. 80 
radians

9
 180 
9
CONVERSIONS BETWEEN DEGREES AND RADIANS
• To rewrite a degree measure in radians, multiply by л radians
180°
• To rewrite a radian measure in degrees, multiply by
180°
л radians
Converting Radians to Degree Measure
36
2  180 
1.
 72


5   radians 
6  180 
2.
 154.3


7   radians 
Arc Length and Area of a Sector
• The arc length s and
area A of a sector with
radius r and central
angle θ (measured
in radians) are as
follows:
r
arc length
s
central
angle

Arc Length: s  r
1 2
Area: A  r 
2
Find the arc length and area of the sector.
  radians 
  60 

 180 
60


3
 
Arc Length: s  10   
3
10

3
Find the arc length and area of the sector.
  radians 
  60 

 180 
60


3
1
2 
Area: A  10   
2
3
50

3