Question

If a person is looking down at an object, the acute angle measured from the horizontal to a line of sight to the object is called the angle of _____.

Short answer

depression

Step-by-step solution

Understand the Line of Sight

Identify the line of sight from the person's eyes to the object. This is an imaginary line that connects the person's eyes to the point they are looking at.

Identify the Horizontal Line

Identify the horizontal line, which is parallel to the ground and passes through the person's eyes.

Measure the Angle

Measure the angle between the horizontal line and the line of sight. This angle is the acute angle mentioned in the problem.

Name the Angle

The acute angle measured from the horizontal to the line of sight when looking down is called the angle of depression.

Key concepts

Line of Sight

The line of sight is an imaginary straight line where your eyes are looking. Imagine you're looking at a tree. The line of sight would be a straight path from your eyes to the tree. In geometry problems, the line of sight helps define other angles and lines. Think of it as a connection from your eyes to what you see.
It's crucial because it helps establish a visual path. By identifying the line of sight, you can understand how different angles and lines relate to each other. For example, in an exercise, this line helps determine the angle of depression.
Identifying the line of sight is usually the first step in problems involving angles and vision. Remember, it’s imaginary, but it helps solve many geometry problems.

Horizontal Line

A horizontal line is a straight line that runs left to right and is parallel to the ground. It doesn’t tilt in any direction. Imagine standing and looking straight ahead. The line that stays at the level of your eyes and doesn’t go up or down is the horizontal line.
This line is essential in geometric problems because it serves as a reference point. In problems dealing with angles, the horizontal line helps measure how much you’re looking up or down. Without it, finding angles like the angle of depression becomes tricky.
In the given problem, the horizontal line intersects with the line of sight to form angles. Identifying this line, which passes through the observer's eye level, is often the second step in solving these exercises.

Acute Angle

An acute angle is any angle less than 90 degrees. These angles are sharp and small compared to right angles or obtuse angles. They appear frequently in various shapes and figures, and understanding them is vital.
In the context of the problem, the angle of depression is an acute angle formed between the horizontal line and the line of sight. Because it’s less than 90 degrees, it falls into this category.
Acute angles are simple yet fundamental in geometry. Recognizing these angles, you can define and solve various problems efficiently. When looking down an object, the acute angle created between your sight and the horizontal, parallel to the ground, is specifically the angle of depression.