Concept 9.3
The Angle of Depression
Source: NCERT Mathematics, Class 108 minute lesson
Formal statement
The angle of depression of an object below the eye is the angle between the horizontal line through the eye and the line of sight down to the object. It equals the angle of elevation of the eye seen from the object.
The intuition
From the top of a cliff you look down at a boat. Start from looking straight out, horizontally, and tilt down: that tilt is the angle of depression.
The horizontal at the top and the ground are parallel, so the angle of depression equals the angle of elevation from the boat (alternate angles). Put it at the boat and the usual right triangle appears.
The attention
Look at the horizontal line at the top, not the cliff.
Measure from the horizontal at the eye, not from the cliff face
Look hereNot here
- Look here
- Measured from the horizontal. Depression is measured down from the horizontal at the eye. Because that line is parallel to the ground, the same angle reappears at the boat.
- Not here
- Measured from the vertical. Measuring from the cliff face gives 90° minus the angle, and every ratio after that is wrong.
- What it teaches
- Parallel lines let an angle move to where it is more useful.