medium difficulty7 min

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.

In one line: Elevation means going up, so start from the horizontal and move upward.

Practice This Concept

Understand it

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.

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.

Formula and rule

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

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

1A student sees the top of a tower by looking upward from level ground.
2If 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 you can reuse

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

Sketch it in your answer

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer

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.

Common wrong answer

A common wrong answer is to mark the angle with the vertical tower side.

Why it loses marks: Elevation is always measured from the horizontal.

Don't mix this up

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

Exam tip

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

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

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.

1
Enough for 1 mark
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
Add for 2 marks
That upward angle is called the angle of elevation.
3
Add for 3 marks
It is always measured from the horizontal upward, not from the ground directly unless the ground is horizontal.

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