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 / BaseIn 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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Answered: A ladder 20 feet long leans against a…

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

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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Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Question

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.

Figure in plane geometry formed by two rays or lines that share a common endpoint, called the vertex. The angle is measured in degrees using a protractor. The different types of angles are acute, obtuse, right, straight, and reflex.

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