Chapter 13 Sec 1
Right Triangle
Trigonometry
Algebra 2 Chapter 13 Section 1
Trigonometric Ratios
•
The ratios of the sides of the right triangle can
be used to define the trigonometric ratios.
•
The ratio of the side opposite θ and the
hypotenuse is known as sine.
•
The ratio of the side adjacent θ and the
hypotenuse is known as cosine.
•
The ratio of the side opposite θ and the side
adjacent θ is known as tangent.
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Algebra 2 Chapter 13 Section 1
Right Triangle Trigonometry
• Let’s consider a right triangle, one of whose acute angles is θ
• The three sides of the triangle are the hypotenuse, the side
opposite θ, and the side adjacent to θ .
SOH CAH TOA
opp
sin  
hyp
adj
cos  
hyp
hyp
1
csc  

opp sin 
hypotenuse

opp
tan  
adj
hyp
1
sec  

adj cos 
opposite
adjacent
adj
1
cot  

opp tan 
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Algebra 2 Chapter 13 Section 1
Example 1
Find the values of the sine, cosine, and tangent for A.
C
First find the length of AC.
(AB)2 + (BC)2 = (AC)2
152 + 82 = 289 = (AC)2
AC = 17
17 cm
8 cm
B
15 cm
adj 15
cos A 

hyp 17
opp 8
tan A 

adj 15
opp 8
sin A 

hyp 17
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A
Algebra 2 Chapter 13 Section 1
Special Values
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Algebra 2 Chapter 13 Section 1
Example 2
Write an equation involving sin, cos, or tan that could
be used to find the value of x. Then solve the equation.
Round to the nearest tenth.
adj
cos  
hyp
x
cos 30 
8
3 x

2
8
8
30°
x
x4 3
8 3
x
2
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Algebra 2 Chapter 13 Section 1
Example 3
Solve ∆XYZ. Round measures of
the sides to the nearest tenth and measures of angles
X
to the nearest degree.
Find x and y
10 35°
x
tan 35 
10
10 tan 35  x
cos 35 
Find Y
10
z
10
z
cos 35
7.0  x
35  Y  90
z
z  12.2
Z
x
Y  55
x  7. 0
z  12.2
Y  55
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Y
Algebra 2 Chapter 13 Section 1
Example 4
Solve ∆ABC. Round measures of the
sides to the nearest tenth and measures of angles to the
B
nearest degree.
Find A
opp 5
sin A 

hyp 13
13
5
C
12
Use a calculator and the SIN–1 function to find the
angle whose sine is 5/13 .
A
A  23
Find B
23  B  90
B  67
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Algebra 2 Chapter 13 Section 1
Example 5
In order to construct a bridge across a river,
the width of the river at the location must be determined.
Suppose a stake is planted on one side of the river directly
across from a second stake on the opposite side. At a distance
30 meters to the right of the stake, an angle of 55°, find the
width of the river.
w
tan 55 
30
30 tan 55  w
w
55°
30 m
w  42.8444 or 42.8 meters
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Algebra 2 Chapter 13 Section 1
Elevation and Depression
•
•
•
•
There are many applications requiring
trigonometric solutions. A prime example
would be surveyors use of special
instruments to find the measures of angles
of elevation and angles of depression.
Angle of elevations is the angle between a horizontal line and
the line of sight from an observer to an object at a higher level.
Angle of depression is the angle between a horizontal line and
the line of sight from the observer to an object at a lower level.
These two are equal measures because they are alternate
interior angles.
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Algebra 2 Chapter 13 Section 1
Example 6
The Aerial run in Snowbird,
Utah, has an angle of elevation of 20.2°. It’s
vertical drop is 2900 feet. Estimate the length of
this run.
2900
sin 20.2 
l
2900
l
sin 20.2
l  8398.5 feet
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Algebra 2 Chapter 13 Section 1
Daily Assignment
•
Chapter 13 Section 1
•
Study Guide
•
Pg 175 – 176 All
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