8­5 Angle of Elevation and Depression 2011
February 14, 2011
8.5 Angles of Elevation and Depression
Objective:
Use angles of elevation and depression to solve problems.
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8­5 Angle of Elevation and Depression 2011
February 14, 2011
Warm Up
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8­5 Angle of Elevation and Depression 2011
February 14, 2011
Vertical heights can be measured using either the
angle of elevation or the angle of depression.
Object
Li
of
ne ht
sig
Angle of elevation
Horizontal
Angle of depression
Li
o
ne
t
igh
f s
Object
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8­5 Angle of Elevation and Depression 2011
February 14, 2011
Suppose a person on the ground sees a
hot-air balloon at a 38o angle above a
horizontal line.
horizontal line
angle of depression
38
o
This is the angle of elevation.
At the same time, the hot-air balloon
sees the person on the ground at a 38o
angle below a horizontal line.
This is the angle of depression.
38o
angle of elevation
horizontal line
Why are the angles equal?
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8­5 Angle of Elevation and Depression 2011
February 14, 2011
Identify angles 1 - 4 as angles of elevation
or angles of depression.
1
2
3
4
5
8­5 Angle of Elevation and Depression 2011
February 14, 2011
A surveyor levels a theodolite (a surveying
tool) with the bottom of the arch.
From there, she measures the angle of
elevation to the top of the arch.
She then measures the distance from where
she stands to a point directly under the
arch.
What is the height of the arch?
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8­5 Angle of Elevation and Depression 2011
February 14, 2011
o
You sight a rock climber on a cliff at a 32 angle of elevation.
The horizontal ground distance to the cliff is 1000 ft.
Find the line-of-sight distance to the rock climber.
x
32o
1000
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8­5 Angle of Elevation and Depression 2011
February 14, 2011
To approach runway 17 of the Ponca City Municipal Airport in
Oklahoma, the pilot must begin a 3o descent starting from an altitude of
2714 ft. The airport altitude is 1007 ft.
How many miles from the runway is the airplane at the start of this
approach?
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8­5 Angle of Elevation and Depression 2011
February 14, 2011
Homework:
page 447
(1 - 14, 28, 35 - 37)
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