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A ladder 20 feet long leans against a building, forming an angle 71 degrees with the level ground. To the nearest foot, how high up the wall of the building does the ladder touch the building?

A ladder 20 feet long leans against a building, forming an angle 71 degrees with the level ground. To the nearest foot, how high up the wall of the building does the ladder touch the building?

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.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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A ladder 20 feet long leans against a building, forming an angle 71 degrees with the level ground. To the nearest foot, how high up the wall of the building does the ladder touch the building?
### Understanding Triangles: An Educational Diagram #### Diagram Description: In the provided diagram, we observe a right triangle formed by a vertical line, a diagonal line, and a horizontal line. Below is a detailed breakdown of its components: 1. **Vertical Line:** - Labeled with a height of 7. - Represents one leg of the right triangle. 2. **Diagonal Line:** - The hypotenuse of the triangle. - Measures 20 feet in length. - Forms an angle of 71 degrees with the horizontal line. 3. **Horizontal Line:** - Represents the base of the right triangle. - Perpendicular to the vertical line and forms a 90-degree angle with it. #### Angles and Measurements: - The angle between the diagonal line (hypotenuse) and the horizontal base of the triangle is noted as 71 degrees. - The vertical leg of the triangle has a height of 7 units (no specific unit is mentioned, but typically could be feet, meters, etc.) - The hypotenuse measures 20 feet. #### Educational Focus: This diagram serves as a foundational example of a right triangle where: - Pythagoras' theorem applies (a² + b² = c²). - Trigonometric ratios such as sine, cosine, and tangent can be explored for angle and side calculations. **Important Equations:** - **Sine (sin θ):** Opposite / Hypotenuse = Height / Hypotenuse - **Cosine (cos θ):** Adjacent / Hypotenuse = Base / Hypotenuse - **Tangent (tan θ):** Opposite / Adjacent = Height / Base In this triangle: - sin(71°) can be calculated as 7 / 20. - cos(71°) can be defined as the length of the base / 20. Understanding this diagram is crucial for grasping basic trigonometric concepts and their applications in real-world scenarios such as construction, navigation, and physics.
Transcribed Image Text:### Understanding Triangles: An Educational Diagram #### Diagram Description: In the provided diagram, we observe a right triangle formed by a vertical line, a diagonal line, and a horizontal line. Below is a detailed breakdown of its components: 1. **Vertical Line:** - Labeled with a height of 7. - Represents one leg of the right triangle. 2. **Diagonal Line:** - The hypotenuse of the triangle. - Measures 20 feet in length. - Forms an angle of 71 degrees with the horizontal line. 3. **Horizontal Line:** - Represents the base of the right triangle. - Perpendicular to the vertical line and forms a 90-degree angle with it. #### Angles and Measurements: - The angle between the diagonal line (hypotenuse) and the horizontal base of the triangle is noted as 71 degrees. - The vertical leg of the triangle has a height of 7 units (no specific unit is mentioned, but typically could be feet, meters, etc.) - The hypotenuse measures 20 feet. #### Educational Focus: This diagram serves as a foundational example of a right triangle where: - Pythagoras' theorem applies (a² + b² = c²). - Trigonometric ratios such as sine, cosine, and tangent can be explored for angle and side calculations. **Important Equations:** - **Sine (sin θ):** Opposite / Hypotenuse = Height / Hypotenuse - **Cosine (cos θ):** Adjacent / Hypotenuse = Base / Hypotenuse - **Tangent (tan θ):** Opposite / Adjacent = Height / Base In this triangle: - sin(71°) can be calculated as 7 / 20. - cos(71°) can be defined as the length of the base / 20. Understanding this diagram is crucial for grasping basic trigonometric concepts and their applications in real-world scenarios such as construction, navigation, and physics.
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