Angle Of Elevation And Depression Worksheet Answers

Understanding Angle of Elevation and Depression

The angle of elevation and depression are fundamental concepts in trigonometry, widely used in various real-world applications such as physics, engineering, and geography. In this article, we will delve into the definitions, differences, and applications of these angles, along with providing a comprehensive worksheet for practice.

Angle of Elevation

The angle of elevation is the angle between the horizontal and the line of sight to an object above the horizontal. It is used to determine the height of an object or the distance between two objects. The angle of elevation is always measured from the horizontal plane.

Example: If you are standing on the ground and looking up at a bird flying overhead, the angle between the ground and your line of sight to the bird is the angle of elevation.

Angle of Depression

The angle of depression is the angle between the horizontal and the line of sight to an object below the horizontal. It is used to determine the depth of an object or the distance between two objects. The angle of depression is always measured from the horizontal plane.

Example: If you are standing on a cliff and looking down at a boat in the water below, the angle between the horizontal and your line of sight to the boat is the angle of depression.

Key Differences

Worksheet Answers

Here are the answers to a comprehensive worksheet on angle of elevation and depression:

Section 1: Multiple Choice

1. What is the angle between the horizontal and the line of sight to an object above the horizontal? a) Angle of depression b) Angle of elevation c) Right angle d) Oblique angle

Answer: b) Angle of elevation

1. Which angle is used to determine the depth of an object? a) Angle of elevation b) Angle of depression c) Right angle d) Oblique angle

Answer: b) Angle of depression

Section 2: Short Answer

1. Define the angle of elevation and provide an example.

Answer: The angle of elevation is the angle between the horizontal and the line of sight to an object above the horizontal. Example: If you are standing on the ground and looking up at a bird flying overhead, the angle between the ground and your line of sight to the bird is the angle of elevation.

1. Define the angle of depression and provide an example.

Answer: The angle of depression is the angle between the horizontal and the line of sight to an object below the horizontal. Example: If you are standing on a cliff and looking down at a boat in the water below, the angle between the horizontal and your line of sight to the boat is the angle of depression.

Section 3: Problems

1. If the angle of elevation to the top of a building is 60°, and the distance from the observer to the building is 50 meters, what is the height of the building?

Answer: Using trigonometry, we can find the height of the building: height = distance × tan(angle) = 50 × tan(60°) = 50 × √3 = 86.6 meters

1. If the angle of depression to a boat in the water is 30°, and the distance from the observer to the boat is 20 meters, what is the depth of the boat?

Answer: Using trigonometry, we can find the depth of the boat: depth = distance × tan(angle) = 20 × tan(30°) = 20 × √3/3 = 11.55 meters

📝 Note: These problems require the use of trigonometric functions, such as tangent, to solve.

In conclusion, understanding the angle of elevation and depression is crucial in various fields, including physics, engineering, and geography. By mastering these concepts, you can solve problems involving height, distance, and depth with ease.