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Angle of Elevation and Depression
Angle of elevation is the angle up from the horizontal to a line of sight (you look up at a tower). Angle of depression is the angle down from the horizontal (you look down from a cliff). The two are equal when they are alternate angles on parallel horizontals.
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Angle of Elevation and Depression
What is it?
Angle of elevation is the angle up from the horizontal to a line of sight (you look up at a tower). Angle of depression is the angle down from the horizontal (you look down from a cliff). The two are equal when they are alternate angles on parallel horizontals.
In simple words
Angle of Elevation and Depression is a core idea in this chapter. Learn the meaning first, then the main parts, then one clear example.
Examples
- Tree height from a measured base
- Kite string as hypotenuse
- Building across a road
ELEVATION
From your eye, draw a horizontal. The angle between that line and the line to the top of the object is elevation. Use tan = opposite/adjacent in the right triangle: height / distance.
DEPRESSION
From a high point, the horizontal is still the reference. Depression to a boat is the same size as the elevation from the boat to you, because the two horizontals are parallel. Do not measure from the vertical.
Recommended for Class 9
Full school-level explanation
Angle of elevation is the angle up from the horizontal to a line of sight (you look up at a tower). Angle of depression is the angle down from the horizontal (you look down from a cliff). The two are equal when they are alternate angles on parallel horizontals.
Draw the horizontal first:
ELEVATION
From your eye, draw a horizontal. The angle between that line and the line to the top of the object is elevation. Use tan = opposite/adjacent in the right triangle: height / distance.
Remember
- horizontal at the eye
- tan = height/distance
Examples
- Tree height from a measured base
- Kite string as hypotenuse
- Building across a road
DEPRESSION
From a high point, the horizontal is still the reference. Depression to a boat is the same size as the elevation from the boat to you, because the two horizontals are parallel. Do not measure from the vertical.
Remember
- parallel horizontals
- alternate angles
Examples
- Cliff to a ship
- Window down to a car
- Do not use the zenith angle by mistake
Remember
- from the horizontal
- elevation up
- depression down
- bearing is from north
- sketch the horizontal
- horizontal at the eye
- tan = height/distance
- parallel horizontals
How the ideas connect
A bearing is a different idea: direction from north, clockwise, usually as three figures (050 deg). Elevation is up and down, not compass heading.
Deeper understanding
Go beyond memorising Angle of Elevation and Depression. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
A bearing is a different idea: direction from north, clockwise, usually as three figures (050 deg). Elevation is up and down, not compass heading.
Exam focus
Quick revision
- from the horizontal
- elevation up
- depression down
- bearing is from north
- ELEVATION: From your eye, draw a horizontal. The angle between that line and the line to the top of the object
- DEPRESSION: From a high point, the horizontal is still the reference. Depression to a boat is the same size as t
Always state which horizontal you used. A sketch with a right angle and the horizontal marked scores method marks even before the arithmetic.
For long answers on Angle of Elevation and Depression: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- from the horizontal
- elevation up
- depression down
- bearing is from north
Important formulas
- from the horizontal
- elevation up
- depression down
Common exam traps
- Always state which horizontal you used. A sketch with a right angle and the horizontal marked scores method marks even before the arithmetic.
- Always state which horizontal you used. A sketch with a right angle and the horizontal marked scores method marks even before the arithmetic.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Always state which horizontal you used. A sketch with a right angle and the horizontal marked scores method marks even before the arithmetic.
- Mistake
Always state which horizontal you used. A sketch with a right angle and the horizontal marked scores method marks even before the arithmetic.
- Mistake
Always state which horizontal you used. A sketch with a right angle and the horizontal marked scores method marks even before the arithmetic.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
from the horizontal
elevation up
depression down
bearing is from north
Angle of elevation is the angle up from the horizontal to a line of sight (you look up at a tower). Angle of depression is the angle down from the horizontal (y
tan = height/distance
- Definition
- Angle of elevation is the angle up from the horizontal to a line of sight (you look up at a tower). Angle of depression is the angle down from the horizontal (y
- Formula
- tan = height/distance
- Example
- Tree height from a measured base
- Critical warning
- Always state which horizontal you used. A sketch with a right angle and the horizontal marked scores method marks even b
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Exam Practice
Define
Q1. Define Angle of Elevation and Depression.
Explain
Q2. Explain: ELEVATION.
Example
Q3. Give one clear example of Angle of Elevation and Depression and say why it fits.
Mistake
Q4. State one common mistake students make about Angle of Elevation and Depression.
Exam note
Q5. Write a short exam note on Angle of Elevation and Depression: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.