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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.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter5: Similar Triangles
Section5.3: Proving Triangles Similar
Problem 41E: Prove that the altitude drawn to the hypotenuse of a right triangle separates the right triangle...
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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.
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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