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Angle of Elevation

An angle of elevation is a measure of the vertical angle between the horizontal plane and a line of sight to an object above the horizontal plane. In other words, it is the angle formed by a horizontal line and a line drawn from the observer’s eye to an object above the observer’s position.

The angle of elevation is often used in geometry and trigonometry to solve problems involving heights and distances. It is a useful tool in fields such as surveying, astronomy, and navigation, as it allows us to determine the height of an object or the distance between the object and the observer.

Definitions

• Angle of Elevation: The angle formed by a horizontal line and a line drawn from the observer’s eye to an object above the observer’s position.
• Horizontal Plane: A flat, level surface that is parallel to the ground.
• Line of Sight: A line drawn from the observer’s eye to an object.
• Observer: The person or object viewing an object from a particular position.

Examples

1. Determining the Height of a Building

Imagine you are standing on the ground looking up at a tall building. The angle of elevation from your eye to the top of the building is 30 degrees. If you know the distance from your position to the base of the building, you can use trigonometry to calculate the height of the building.

2. Shooting a Cannon

In military or naval warfare, the angle of elevation is used to determine the trajectory of a cannonball. The angle of elevation is adjusted to account for wind speed, air resistance, and other factors that affect the flight of the cannonball.

3. Measuring the Distance to a Mountain

Suppose you are standing on a flat plain and looking at a distant mountain. If you know the angle of elevation from your eye to the top of the mountain, and you also know the height of the mountain, you can use trigonometry to calculate the distance from your position to the base of the mountain.

4. Astronomy

In astronomy, the angle of elevation is used to determine the position of celestial objects in the sky. By measuring the angle of elevation of a particular star or planet, astronomers can calculate its distance from the Earth and its position in the sky.

5. Surveying

Surveyors use the angle of elevation to measure the height of landforms, such as hills and mountains. By measuring the angle of elevation from a flat, level surface to the top of a landform, surveyors can calculate the height of the landform.

Quiz

1. What is an angle of elevation?
2. How is an angle of elevation used in geometry and trigonometry?
3. In what fields is the angle of elevation useful?
4. How can the angle of elevation be used to determine the height of a building?
5. How is the angle of elevation used in military or naval warfare?
6. How can the angle of elevation be used to measure the distance to a mountain?
7. How is the angle of elevation used in astronomy?
8. How is the angle of elevation used in surveying?
9. What is a horizontal plane?
10. What is a line of sight?