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Angle of elevation

The angle of elevation is the angle made by the line of sight with the horizontal when an object is seen above eye level.

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Student-friendly explanation

When you look at the top of a tree, tower, or building from a lower position, your eyes look upward. The horizontal line at your eye level and the slant line to the object form an angle. That upward angle is called the angle of elevation. It is always measured from the horizontal upward, not from the ground directly unless the ground is horizontal.

How to write this in exams

  1. 1

    Start with the exact idea

    The angle of elevation is the angle made by the line of sight with the horizontal when an object is seen above eye level.

  2. 2

    Then show how to use it

    1. Locate the observer. 2. Draw the horizontal through the eye. 3. Draw the line of sight to the object. 4. Mark the angle between them on the upward side. 5. Name it as angle of elevation.

  3. 3

    Add one concrete example

    If a student stands on level ground and looks at the top of a flagpole, the angle between the horizontal line from the eyes and the line of sight to the top is the angle of elevation.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is to mark the angle with the vertical tower side. That is wrong because elevation is always measured from the horizontal.

Definition

The angle of elevation is the angle made by the line of sight with the horizontal when an object is seen above eye level.

Example

If a student stands on level ground and looks at the top of a flagpole, the angle between the horizontal line from the eyes and the line of sight to the top is the angle of elevation.

Rule to remember

Angle of elevation = angle between the horizontal and the line of sight when the object is above the observer.

Memory hook

Elevation means going up, so start from the horizontal and move upward.

Examples and method

Worked example

A student sees the top of a tower by looking upward from level ground. If the horizontal line is drawn through the student's eye and the line of sight rises to the tower top, the marked upward angle is the angle of elevation.

Method to apply

1. Locate the observer. 2. Draw the horizontal through the eye. 3. Draw the line of sight to the object. 4. Mark the angle between them on the upward side. 5. Name it as angle of elevation.

Diagram support

Draw the observer, a horizontal line through the eye, and a slant line going upward to the object. Mark the angle at the observer.

How CBSE asks it

Find the angle of elevation from a diagram, or identify which angle is the angle of elevation in a tower or building figure.

Avoid common mistakes

Common confusion

Students often measure the angle from the vertical side or from the ground slope instead of from the horizontal line of sight.

Common wrong answer

A common wrong answer is to mark the angle with the vertical tower side. That is wrong because elevation is always measured from the horizontal.

Exam tip

Always draw the horizontal line at the observer's eye level first. Then mark the upward angle carefully.

Quick check

When a student looks up at the top of a school building, from which line is the angle of elevation measured?

The angle of elevation is measured from the horizontal line at the observer's eye level up to the line of sight to the object. It is not measured from the vertical side.

Answer writing and exam use

1-mark answer

The angle of elevation is the angle made by the line of sight with the horizontal when an object is seen above eye level.

2-mark answer

The angle of elevation is the angle made by the line of sight with the horizontal when an object is seen above eye level. Angle of elevation = angle between the horizontal and the line of sight when the object is above the observer. If a student stands on level ground and looks at the top of a flagpole, the angle between the horizontal line from the eyes and the line of sight to the top is the angle of elevation.

3-mark answer

When you look at the top of a tree, tower, or building from a lower position, your eyes look upward. The horizontal line at your eye level and the slant line to the object form an angle. That upward angle is called the angle of elevation. It is always measured from the horizontal upward, not from the ground directly unless the ground is horizontal. Angle of elevation = angle between the horizontal and the line of sight when the object is above the observer. A student sees the top of a tower by looking upward from level ground. If the horizontal line is drawn through the student's eye and the line of sight rises to the tower top, the marked upward angle is the angle of elevation. Find the angle of elevation from a diagram, or identify which angle is the angle of elevation in a tower or building figure. A common wrong answer is to mark the angle with the vertical tower side. That is wrong because elevation is always measured from the horizontal.
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