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What is Angle of Elevation?

Angle of elevation is a term used in geometry and trigonometry that refers to the angle formed by a horizontal line and a line of sight to an object above the horizontal line. The angle is measured from the horizontal line, and it is used to describe the position of an object in relation to an observer. In other words, the angle of elevation is the angle at which an observer must look up to see an object.

Angle of elevation is often used to describe the height of tall objects, such as buildings, trees, and mountains. It is also used in fields such as aviation and surveying to measure the altitude of aircraft and determine the slope of land.

Examples of Angle of Elevation

1. Determining the height of a building: Imagine that you are standing on the ground looking up at the top of a tall building. The angle of elevation to the top of the building is the angle at which you must look up to see the top of the building. By measuring the angle of elevation and knowing the distance from the base of the building to where you are standing, you can use trigonometry to calculate the height of the building.
2. Measuring the altitude of an aircraft: Angle of elevation is also used in aviation to determine the altitude of an aircraft. A pilot or air traffic controller may use a device called a theodolite to measure the angle of elevation to an aircraft in the sky. By knowing the distance between the theodolite and the aircraft and the angle of elevation, the altitude of the aircraft can be calculated.
3. Determining the slope of a hill: Surveyors often use angle of elevation to determine the slope of a hill or other piece of land. By measuring the angle of elevation at different points on the slope, the slope can be calculated and a topographic map can be created.
4. Calculating the height of a tree: Suppose you are standing in a field and you want to determine the height of a tall tree. You can use a clinometer, which is a device that measures angles of elevation, to measure the angle of elevation to the top of the tree. By knowing the distance from the base of the tree to where you are standing and the angle of elevation, you can use trigonometry to calculate the height of the tree.
5. Estimating the height of a mountain: Angle of elevation can also be used to estimate the height of a mountain. For example, if you are standing at the base of a mountain and you know the distance from the base to the peak, you can use a clinometer to measure the angle of elevation to the peak. By knowing the distance and the angle of elevation, you can use trigonometry to calculate the height of the mountain.

Quiz on Angle of Elevation

What is angle of elevation?

The angle formed by a horizontal line and a line of sight to an object above the horizontal line.

What is the angle of elevation to the top of a building if an observer is standing 50 meters from the base of the building and the angle of elevation is 30 degrees?

The height of the building is 25 meters

An observer is standing 100 meters away from the base of a mountain and the angle of elevation to the peak is 45 degrees. What is the height of the mountain?

The height of the mountain is 70.7 meters