Application Activity Angles at the Airport Two terms that are often used when computing distances are the angle of elevation and the angle of depression. They represent the angles formed by a person's line of sight and the horizontal when he or she is looking up or down at an object. Horizon Line of Sight Angle of Elevation Angle of Depression Line of Sight Horizon Example If a person sees an aircraft flying at 3,000 feet with an angle of elevation of 70°, what is the distance to a spot on the ground directly beneath the airplane? opposite leg adjacent leg tangent 3,000 ft tan 70° = Solution (tan 70°) (x) = 3,000 tan 70° %3D 1091.9107 The distance is about 1,092 feet. Solve each problem. Round answers to the nearest unit. 1. A flight controller looks down from the top of the airport tower at an airplane on the runway 3,000 feet from the base of the tower. If the angle of depression is 3°, how tall is the tower? 2. An airplane is taking off at an angle of 9° and travelling at a speed of 200 feet per second in relation to the ground. If clouds begin at altitude of 4,000 feet, how many seconds will it take for the airplane to be in the clouds? 3. An air traffic controller on top of a 300-foot airport tower looks up and sees a balloon. The angle of elevation is 55°. If the balloon is directly above a truck 200 feet from the tower, how high above the ground is the balloon?
Application Activity Angles at the Airport Two terms that are often used when computing distances are the angle of elevation and the angle of depression. They represent the angles formed by a person's line of sight and the horizontal when he or she is looking up or down at an object. Horizon Line of Sight Angle of Elevation Angle of Depression Line of Sight Horizon Example If a person sees an aircraft flying at 3,000 feet with an angle of elevation of 70°, what is the distance to a spot on the ground directly beneath the airplane? opposite leg adjacent leg tangent 3,000 ft tan 70° = Solution (tan 70°) (x) = 3,000 tan 70° %3D 1091.9107 The distance is about 1,092 feet. Solve each problem. Round answers to the nearest unit. 1. A flight controller looks down from the top of the airport tower at an airplane on the runway 3,000 feet from the base of the tower. If the angle of depression is 3°, how tall is the tower? 2. An airplane is taking off at an angle of 9° and travelling at a speed of 200 feet per second in relation to the ground. If clouds begin at altitude of 4,000 feet, how many seconds will it take for the airplane to be in the clouds? 3. An air traffic controller on top of a 300-foot airport tower looks up and sees a balloon. The angle of elevation is 55°. If the balloon is directly above a truck 200 feet from the tower, how high above the ground is the balloon?
College Physics
10th Edition
ISBN:9781285737027
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Introduction
Section: Chapter Questions
Problem 48P
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Transcribed Image Text:Application Activity
Angles at the Airport
Two terms that are often used when computing distances are the
angle of elevation and the angle of depression. They represent
the angles formed by a person's line of sight and the horizontal
when he or she is looking up or down at an object.
Horizon
Line of Sight
Angle of Elevation
Angle of Depression
Line of Sight
Horizon
Example
If a person sees an aircraft flying at 3,000 feet with
an angle of elevation of 70°, what is the distance to
a spot on the ground directly beneath the airplane?
opposite leg
adjacent leg
tangent
3,000 ft
tan 70° =
Solution
(tan 70°) (x) = 3,000
tan 70°
%3D
1091.9107
The distance is about 1,092 feet.
Solve each problem. Round answers to the nearest unit.
1. A flight controller looks down from the top of the airport
tower at an airplane on the runway 3,000 feet from the base
of the tower. If the angle of depression is 3°, how tall is the
tower?
2. An airplane is taking off at an angle of 9° and travelling at a
speed of 200 feet per second in relation to the ground. If
clouds begin at altitude of 4,000 feet, how many seconds will
it take for the airplane to be in the clouds?
3. An air traffic controller on top of a 300-foot airport tower
looks up and sees a balloon. The angle of elevation is 55°. If
the balloon is directly above a truck 200 feet from the tower,
how high above the ground is the balloon?
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