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Line of sight

The line of sight is the straight line joining the observer's eye to the object being seen.

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Student-friendly explanation

In trigonometry problems, the line of sight is the slant line that connects the observer and the target object. It is the key line used to form the angle of elevation or depression. Without this line, we cannot build the right triangle needed for height and distance questions. The line of sight is always straight, not curved, because we imagine the shortest viewing path.

How to write this in exams

  1. 1

    Start with the exact idea

    The line of sight is the straight line joining the observer's eye to the object being seen.

  2. 2

    Then show how to use it

    1. Mark the observer's eye. 2. Mark the target object point. 3. Join them with a straight slant line. 4. Label that line as the line of sight. 5. Use it with the horizontal to form the angle.

  3. 3

    Add one concrete example

    If a student at ground level sees the top of a lamp post, the straight line from the eye to the lamp post top is the line of sight.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is to treat the ground distance as the line of sight. The ground distance is only the adjacent side, not the viewing line.

Definition

The line of sight is the straight line joining the observer's eye to the object being seen.

Example

If a student at ground level sees the top of a lamp post, the straight line from the eye to the lamp post top is the line of sight.

Rule to remember

Line of sight is the straight slant line from eye to object; it helps create the right triangle for trigonometric ratios.

Memory hook

Sight line means the straight line your eyes follow to the object.

Examples and method

Worked example

A person standing on the ground sees the top of a tree. The straight segment from the eye to the top of the tree is the line of sight, and together with the horizontal and vertical it forms a right triangle.

Method to apply

1. Mark the observer's eye. 2. Mark the target object point. 3. Join them with a straight slant line. 4. Label that line as the line of sight. 5. Use it with the horizontal to form the angle.

Diagram support

Draw a straight slant segment from the observer's eye to the top or target point of the object. Label it clearly as line of sight.

How CBSE asks it

Questions ask you to identify the line of sight in a diagram, or to use it indirectly when forming a trigonometric ratio.

Avoid common mistakes

Common confusion

Students sometimes confuse the line of sight with the ground distance or with a ladder leaning against a wall.

Common wrong answer

A common wrong answer is to treat the ground distance as the line of sight. The ground distance is only the adjacent side, not the viewing line.

Exam tip

Mark the line of sight first in every sketch. It helps you find the angle and the right triangle quickly.

Quick check

In a height-and-distance problem, what does the line of sight connect?

The line of sight is the straight line joining the observer's eye and the object being observed. It is the slant side used to form the viewing triangle.

Answer writing and exam use

1-mark answer

The line of sight is the straight line joining the observer's eye to the object being seen.

2-mark answer

The line of sight is the straight line joining the observer's eye to the object being seen. Line of sight is the straight slant line from eye to object; it helps create the right triangle for trigonometric ratios. If a student at ground level sees the top of a lamp post, the straight line from the eye to the lamp post top is the line of sight.

3-mark answer

In trigonometry problems, the line of sight is the slant line that connects the observer and the target object. It is the key line used to form the angle of elevation or depression. Without this line, we cannot build the right triangle needed for height and distance questions. The line of sight is always straight, not curved, because we imagine the shortest viewing path. Line of sight is the straight slant line from eye to object; it helps create the right triangle for trigonometric ratios. A person standing on the ground sees the top of a tree. The straight segment from the eye to the top of the tree is the line of sight, and together with the horizontal and vertical it forms a right triangle. Questions ask you to identify the line of sight in a diagram, or to use it indirectly when forming a trigonometric ratio. A common wrong answer is to treat the ground distance as the line of sight. The ground distance is only the adjacent side, not the viewing line.
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