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The base of the ladder in the figure is a = 12ft from the building, and the angle formed by the ladder and the ground is 71°. How high up the building does the ladder touch? (Round your answer to one decimal place.)

The base of the ladder in the figure is a = 12ft from the building, and the angle formed by the ladder and the ground is 71°. How high up the building does the ladder touch? (Round your answer to one decimal place.)

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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The base of the ladder in the figure is a = 12ft from the building, and the angle formed by the ladder and the ground is 71°. How high up the building does the ladder touch? (Round your answer to one decimal place.)

In the given image, we see a visual representation of a ladder leaning against a building. The image is intended to illustrate the angles and distances involved in problems typically encountered in physics or trigonometry. **Diagram Explanation:** 1. **Ladder**: The ladder is depicted as a long, straight object resting against the building. It is positioned at an angle relative to the ground and extends upward to a window or higher point on the brick building's wall. 2. **Building**: The building is shown as a brick structure with multiple windows arranged in a grid-like pattern. 3. **Ground Distance (a)**: At the bottom of the image, a horizontal red arrow marked with 'a' indicates the distance from the base of the building to the point where the ladder touches the ground. 4. **Angle (θ)**: Near the base of the ladder, an angle θ (theta) is shown. This angle represents the angle between the ladder and the ground. This is a crucial parameter in problems involving static equilibrium and force calculations. This diagram is particularly useful in educational contexts where students need to understand the relationships between angles, distances, and heights in practical scenarios. It might be used in topics such as: - Trigonometry, where students calculate the height the ladder reaches on the building using the sine or cosine of the angle θ. - Physics, to discuss forces acting on the ladder and how these forces relate to tipping risks or the friction between the ladder and the ground. Understanding this diagram helps students visualize and solve real-world problems by applying mathematical and physical principles.
Transcribed Image Text:In the given image, we see a visual representation of a ladder leaning against a building. The image is intended to illustrate the angles and distances involved in problems typically encountered in physics or trigonometry. **Diagram Explanation:** 1. **Ladder**: The ladder is depicted as a long, straight object resting against the building. It is positioned at an angle relative to the ground and extends upward to a window or higher point on the brick building's wall. 2. **Building**: The building is shown as a brick structure with multiple windows arranged in a grid-like pattern. 3. **Ground Distance (a)**: At the bottom of the image, a horizontal red arrow marked with 'a' indicates the distance from the base of the building to the point where the ladder touches the ground. 4. **Angle (θ)**: Near the base of the ladder, an angle θ (theta) is shown. This angle represents the angle between the ladder and the ground. This is a crucial parameter in problems involving static equilibrium and force calculations. This diagram is particularly useful in educational contexts where students need to understand the relationships between angles, distances, and heights in practical scenarios. It might be used in topics such as: - Trigonometry, where students calculate the height the ladder reaches on the building using the sine or cosine of the angle θ. - Physics, to discuss forces acting on the ladder and how these forces relate to tipping risks or the friction between the ladder and the ground. Understanding this diagram helps students visualize and solve real-world problems by applying mathematical and physical principles.
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