MathematicsChapter 6: Trigonometry and Bearing
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).
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 (you look down from a cliff). The two are equal when they are alternate angles on parallel horizontals.
Overview
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.
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.
Examples Cliff to a ship · Window down to a car · Do not use the zenith angle by mistake
Explanation
A bearing is a different idea: direction from north, clockwise, usually as three figures (050 deg). Elevation is up and down, not compass heading.
In simple words
Always state which horizontal you used. A sketch with a right angle and the horizontal marked scores method marks even before the arithmetic.
Key points
- from the horizontal
- elevation up
- depression down
- horizontal at the eye
- tan = height/distance
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Angle of Elevation and Depression
Sticky Notes · Quick Revision
Core Idea
- Angle of elevation is the angle up from the horizontal to a line of sight (you look up at a tower).
Key Points
- from the horizontal
- elevation up
- depression down
Simple Check
- Explain angle of elevation and depression in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Always state which horizontal you used. A sketch with a right angle and the horizontal marked scores method marks even before the arithmetic.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- from the horizontal
- elevation up
- depression down
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