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Angle of Depression

The angle of depression is a term used in trigonometry and geometry to describe the angle between the horizontal line of sight and an object that is below the line of sight. This angle is used to calculate the distance of an object from the observer, as well as the height of the object.

Definitions

• Angle of Depression: The angle between the horizontal line of sight and an object that is below the line of sight.
• Horizontal Line of Sight: A line drawn from the observer’s eye level to the horizon.
• Object: A physical thing that exists in the real world, such as a building or tree.
• Distance: The space between two objects or points.
• Height: The distance from the base of an object to its highest point.

Examples

1. A person standing on top of a hill is looking down at a lake at the bottom of the hill. The angle of depression from the person’s line of sight to the lake is the angle between the horizontal line of sight and the surface of the lake.
2. A pilot flying in an airplane at a high altitude is looking down at a city below. The angle of depression from the pilot’s line of sight to the city is the angle between the horizontal line of sight and the roofs of the buildings in the city.
3. A surveyor is standing on top of a mountain and using a device called a theodolite to measure the angle of depression to a point on the ground below. The surveyor can use this measurement to calculate the distance and height of the point on the ground.
4. A person standing on a beach is looking out at a ship on the horizon. The angle of depression from the person’s line of sight to the ship is the angle between the horizontal line of sight and the water line of the ship.
5. A person standing on a bridge is looking down at a boat passing underneath. The angle of depression from the person’s line of sight to the boat is the angle between the horizontal line of sight and the deck of the boat.

Quiz

1. What is the angle of depression?
2. What is the horizontal line of sight?
3. What is an object?
4. What is distance?
5. What is height?
6. Can the angle of depression be used to calculate the distance of an object from the observer?
7. Can the angle of depression be used to calculate the height of an object?
8. Give an example of a situation where the angle of depression might be used.
9. Can the angle of depression be measured with a device called a theodolite?
10. Can the angle of depression be used to calculate the distance and height of a point on the ground?

Answers:

1. The angle between the horizontal line of sight and an object that is below the line of sight.
2. A line drawn from the observer’s eye level to the horizon.
3. A physical thing that exists in the real world, such as a building or tree.
4. The space between two objects or points.
5. The distance from the base of an object to its highest point.
6. Yes.
7. Yes.
8. A person standing on top of a hill looking down at a lake at the bottom of the hill.
9. Yes.
10. Yes