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7-5 Objectives
You will learn to:
Solve problems involving angles of
elevation.
Vocabulary
Angle of Elevation
Elevation
An angle of elevation is the angle formed by a
horizontal line and a line of sight to a point above
the line. In the diagram, 1 is the angle of elevation
from the tower T to the plane P.
Finding Distance by Using Angle of Elevation
The Seattle Space Needle casts a 67meter shadow. If the angle of
elevation from the tip of the shadow
to the top of the Space Needle is
70º, how tall is the Space Needle?
Round to the nearest meter.
Draw a sketch to represent the
given information. Let A
represent the tip of the shadow,
and let B represent the top of
the Space Needle. Let y be the
height of the Space Needle.
Continued
You are given the side adjacent to
A, and y is the side opposite A.
So write a tangent ratio.
y = 67 tan 70° Multiply both sides by 67.
y
184 m
Simplify the expression.
CIRCUS ACTS At the circus, a person in the
audience watches the high-wire routine. A 5-foot-6-inch
tall acrobat is standing on a platform that is 25 feet
off the ground. How far is the audience member
from the base of the platform, if the angle
of elevation from the audience member’s
line of sight to the top of the
acrobat is 27 ?
Make a drawing.
Since QR is 25
feet and RS is 5
feet 6 inches or 5.5 feet, QS is 30.5 feet. Let x represent PQ.
Answer: The audience is about 60 feet from the platform.
DIVING At a diving competition, a 6-foot-tall diver
stands atop the 32-foot platform. The front edge of the
platform projects 5 feet beyond the ends of the pool.
The pool itself is 50 feet in length. A camera is set up
at the opposite end of the pool even with the pool’s
edge. If the camera is angled so that its line of sight
extends to the top of the diver’s head, what is the
camera’s angle of elevation to the nearest degree?
Answer: about 40.2º
A wheelchair ramp is 3 meters long and
inclines at 6 . Find the height of the ramp to the
nearest tenth centimeter.
The angle of depression between the ramp and the horizontal
is 6 . Use trigonometry to find the height of the ramp.
Method 1: The ground and the horizontal level with the
platform to which the ramp extends are parallel. Therefore,
since they are alternate interior angles.
Y
W
Answer: The height of the ramp is about 0.314 meters,
What did you learn today?
How to:
Solve problems involving angles of
elevation.
Assignment:
Page 374
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