Trigonometric Ratios and Problem Solving with Right Triangles

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Trigonometric Ratios andProblem Solving with
Right Triangles

• 13.1 13.2

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Todays Objectives

• Introduce trigonometry
• Discover the sine, cosine, and tangent ratios
• Understand the usefulness of trigonometry
• Learn new vocabulary

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9
x
6
3
31º
31º
31º
31
15
55
10
5




4.5
27
y
9
42º
5
42º
42º
42º
10
30
90
What can we tell about these two sets of
triangles?
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Glossary
Sin
Cos
Tan
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B
Hypotenuse
c
a
Leg opposite A
A
b
C
Leg adjacent to A
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Glossary

• Angle of ElevationIf a person is looking up, the
  angle formed from the horizon to the line of
  sight.

Line of Sight
Horizon
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Angle of DepressionIf a person is looking down,
the angle formed by the horizon down to the line
of sight
Horizon
Line of Sight
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Example A
Find the height of a tree if the angle of
elevation is 40º and the distance to the tree is
36 meters.
Answer We are given an angle and its side
adjacent and need the side opposite. The trig
ratio that will fit this data is the tan. tan 40º

x
40º
36m
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tan 40º
.8391 x /36
(36) (.8391) x
30.2 x
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Example B
Find sin P, cos P, tan P, cos T, and tan T?
R
t
p
T
r
P
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R
t
p
T
r
P
Sin T
Sin P

Cos P

Cos T
Tan T
Tan P

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Example C
To the nearest meter, find the height of a right
trianlge if one acute angle measures 35º and the
adjacent side measures 24 meters.