Imagine you're at a movie theater where the screen is 36 feet tall, mounted on the wall so its bottom edge is 16 feet above the ground. Suppose also that the floor is perpendicular to the wall holding the screen. Depending on where you sit, the movie screen takes up a different angle in your visual field. Consider the angle whose vertex is at your eye, with one side connecting to the top of the screen and the other side to the bottom of the screen. In the image below, the seating position of the viewer is shown as a dot on the horizontal floor. You can interact with the image by clicking and then dragging the viewer's position. As you move the viewer, their distance from the wall and the viewing angle of the whole screen will be shown at the top of the image: Distance from wall = 32.0 feet Viewing angle = 31.83° 36 ft 16 ft Notice that when the person sits far from the wall, the viewing angle is small. As they move closer to the wall, the angle increases, but moving too close will make the angle decrease again. Use the image to approximate the largest viewing angle. The largest angle is about degrees when the person's distance from the wall is about feet.
Imagine you're at a movie theater where the screen is 36 feet tall, mounted on the wall so its bottom edge is 16 feet above the ground. Suppose also that the floor is perpendicular to the wall holding the screen. Depending on where you sit, the movie screen takes up a different angle in your visual field. Consider the angle whose vertex is at your eye, with one side connecting to the top of the screen and the other side to the bottom of the screen. In the image below, the seating position of the viewer is shown as a dot on the horizontal floor. You can interact with the image by clicking and then dragging the viewer's position. As you move the viewer, their distance from the wall and the viewing angle of the whole screen will be shown at the top of the image: Distance from wall = 32.0 feet Viewing angle = 31.83° 36 ft 16 ft Notice that when the person sits far from the wall, the viewing angle is small. As they move closer to the wall, the angle increases, but moving too close will make the angle decrease again. Use the image to approximate the largest viewing angle. The largest angle is about degrees when the person's distance from the wall is about feet.
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Trigonometry
Section1.8: Applications And Models
Problem 4ECP: From the time a small airplane is 100 feet high and 1600 ground feet from its landing runway, the...
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Transcribed Image Text:Imagine you're at a movie theater where the screen is 36 feet tall, mounted on the wall so its bottom edge is 16 feet
above the ground. Suppose also that the floor is perpendicular to the wall holding the screen.
Depending on where you sit, the movie screen takes up a different angle in your visual field. Consider the angle whose
vertex is at your eye, with one side connecting to the top of the screen and the other side to the bottom of the screen.
In the image below, the seating position of the viewer is shown as a dot on the horizontal floor. You can interact with the
image by clicking and then dragging the viewer's position. As you move the viewer, their distance from the wall and the
viewing angle of the whole screen will be shown at the top of the image:
Distance from wall = 32.0 feet
Viewing angle -31.83°
36 ft
16 ft
Notice that when the person sits far from the wall, the viewing angle is small. As they move closer to the wall, the angle
increases, but moving too close will make the angle decrease again.
Use the image to approximate the largest viewing angle.
The largest angle is about
degrees when the person's distance from the wall is about
feet.
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