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Warm Up
Chapter 2
1. Graph y   x  1 x  3  x  4 
2
2. Write an equation for the graph.
3. A rectangular dog pen is constructed using a barn wall
as one side and 60 m of fencing for the other three sides.
Find the dimensions of the pen that give the greatest area.
4. Factor
2
a. 2𝑥 + 𝑥 − 28
2
b. 6𝑥 − 24
Warm Up
Chapter 2
1. Graph y   x  1 x  3  x  4 
2
2. Write an equation for the graph.
Graph y   x  1
3
 x  3
3. A rectangular dog pen is constructed using a barn wall
as one side and 60 m of fencing for the other three sides.
Find the dimensions of the pen that give the greatest area.
A  x   x  60  2 x  , 0  x 
Real-world
domain?
30
A  x   2 x 2  60 x
b
Maximum value will occur at x  
2a
Problem
3. A rectangular dog pen is constructed using a barn wall
as one side and 60 m of fencing for the other three sides.
Find the dimensions of the pen that give the greatest area.
A  x   2x  60x
2
60
x
 15
2  2 
 the maximum area occurs when the dimensions are
15 m by 30 m
A 15  450 m 2
Diagram
4. Factor
2
a. 2𝑥 + 𝑥 − 28
𝟐𝒙 − 𝟕 𝒙 + 𝟒
2
b. 6𝑥 − 24
𝟐
𝟔(𝒙
− 𝟒)
𝟔 𝒙−𝟐 𝒙+𝟐
CHAPTER 9
Triangle Trigonometry
Section 9-1
Solving Right Triangles
Objective: To use trigonometry to
find unknown sides or angles of a
right triangle
These functions can be used for finding
unknown angles or sides of a right triangle.
Labeling Format
B
UPPER CASE
VERTICES
a
c
lower case
sides
A
b
C
Example: Solve the triangle below:
*Solving a triangle means to find the value of ALL angles
and sides.
Solution:
⦟𝐵 = 90° − 28° = 62°
To find the value of b, use tan 28⁰
To find the value of c, use
pythagoraen theorem
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑡𝑎𝑛𝜃 =
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
40
𝑡𝑎𝑛28° =
𝑏
40
𝑏=
≈ 75.2
tan 28⁰
𝑐 2 = 𝑎2 + 𝑏 2
𝑐 2 = 402 + 75.22
𝑐 = 7255.04 ≈ 85.2
Angles of Elevation and Depression
The angle of elevation of an object as seen by an observer is the angle
between the horizontal and the line from the object to the observer's eye
(the line of sight).
If the object is below the level of the observer, then the angle between
the horizontal and the observer's line of sight is called the angle of
depression.
Homework
Worksheet for Section 9.1