Transcript Chapter 8 Right Triangles (page 284)

Trigonometry
Essential Question
How can you apply right triangle
facts to solve real life problems?
Lesson 8-7
Applications of Right
Triangle Trigonometry
(page 317)
A
horizontal
1
B
2
The angles formed between the horizontal and the line of sight are the:
ANGLE of DEPRESSION
∠1
when a point B is viewed from a higher point A, ie. ____.
A
1
B
2
horizontal
The angles formed between the horizontal and the line of sight are the:
ANGLE of ELEVATION
∠2
when a point A is viewed from a lower point B, ie. ____.
Angle of
Elevation
horizontal
Angle of
Depression
Example 1
At a certain time, a post 6 feet tall casts
a 3 feet shadow. What is the angle of
elevation of the sun?
6’
xº
3
See the right triangle.
6
tan xº =
3
-1
x = tan (2)
x » 63.4
6’
xº
3
∴ the angle
of elevation
of the sun is 63º.
Example 2
A person in a lighthouse 22 meters above sea level sights a
boat in the water. If the angle of depression to the boat is
25º, how far from the base of the lighthouse is the boat?
25º
22m
?m
The goal is to get a right triangle!
See the right triangle!
25º
22m
?m
Now use trigonometry.
22
tan 25º =
x
90º - 25º =
65º
x
tan 65º =
22
or
➤
25º
22m
Xm
➤
25º
Solve either equation, they both give the same solution …
22
tan 25º =
x
22
x=
tan25º
x » 47
or
x
tan 65º =
22
x = 22× tan65º
x » 47
∴ the boat is 47 meters from the
base of the lighthouse.
Worksheet on Lesson 8-7
Applications of Trigonometry
Assignment
Written Exercises on pages 318 to 320
REQUIRED: 1 to 13 odd numbers
Prepare for Quiz on Lessons 8-5 to 8-7
How can you apply right triangle
facts to solve real life problems?
Worksheet on Lessons 8-5 to 8-7
Prepare for Quiz on Lessons 8-5 to 8-7
Worksheet on Chapter 8: Right Triangles
Prepare for Test on Chapter 8: Right Triangles
How can you apply right triangle
facts to solve real life problems?