Transcript Applied Geometry

Geometry
Lesson 8 – 5
Angles of Elevation and
Depression
Objective:
Solve problems involving angles of elevation and depression.
Use angles of elevation and depression to find the
distance between two objects.
Elevation and Depression
Angle of Elevation

The angle formed by a horizontal line and an
observer’s line of sight to an object above the
horizontal line
Angle of Depression

The angle formed by a horizontal line and an
observer’s line of sight to an object below the
horizontal line
Be Careful!
Angle of depression can be tricky!
This is not an angle of
depression!
Leah is meeting friends at the castle in the center of
an amusement park. She sights the top of the castle
at an angle of elevation of 38o. From the park’s
brochure, she knows that the castle is 190 feet tall. If
Leah is 5.5 feet tall, about how far is she from the
castle to the nearest foot?
Sketch a picture
184 .5
tan 38 
x
184 .5
x
tan 38
x  236 ft
The cross bar of a goalpost is 10 feet high. If a field
goal attempt is made 25 yards from the base of the
goal post that clears the goal by 1 foot, what is the
smallest angle of elevation at which the ball could
have been kicked to the nearest degree?
10 + 1
11
x
75
11
tan x 
75
11
tan
x
75
1
x  8
A search and rescue team is airlifting people from the scene
of a boating accident when they observe another person in
need of help. If the angle of depression to this other person
is 42o and the helicopter is 18 feet above the water, what is
the horizontal distance from the rescuers to this person to
the nearest foot?
*have students draw
picture on board
18
tan 42 
x
18
x
tan 42
x  20 ft
A life guard is watching a beach from a line of sight
6 feet above the ground. She sees a swimmer at
an angle of depression of 8o. How far away from
the tower is the swimmer?
x
6 feet
6
tan 8 
x
6
x
tan 8
x  43 ft
To estimate the height of a tree she wants removed, Mrs.
Long sights the tree’s top at 70o angle of elevation. She then
steps back 10 meters and sights the top at a 26o angle. If
Mrs. Long’s line of sight is 1.7 meters above the ground, how
tall is the tree to the nearest meter?
x
tan 70 
y
Solve for a variable
y tan70  x
x
tan 26 
10  y
Solve for the same variable
(10  y)(tan26)  x
Cont…
Solve by system of equations
y tan70  x
2.16 tan 70  x
(10  y)(tan26)  x
x  5.93
(10  y)(tan26)  y tan70
5.9 + 1.7 = 7.6
10 tan26  y tan26 y tan70
The height is about
10 tan26  y tan70  y tan26
8 meters.
10 tan26  y(tan70  tan26)
10 tan 26
y
tan 70  tan 26
y  2.16
Two buildings are sited from atop a 200meter skyscraper. Building A is sited at
a 35o angle of depression, while
Building B is sighted at a 36o angle of
depression. How far apart are the two
buildings to the nearest meter?
10 meters
Homework
Pg. 577 1 – 3 all, 4 – 20 EOE,
24, 28 – 48 E