Concept 9.1
The Angle of Elevation
Source: NCERT Mathematics, Class 106 minute lesson
Formal statement
The angle of elevation of an object above the eye is the angle between the horizontal line through the eye and the line of sight to the object.
The intuition
Stand at a distance from a tower and look up at its top. The angle you tilt your head through, starting from looking straight ahead, is the angle of elevation.
Straight ahead means horizontal. So the angle is always measured from the horizontal line, never from the tower or the vertical.
The attention
Look at the horizontal line through the eye: the angle starts there.
Angle between the horizontal and the line of sight, not the tower
Look hereNot here
- Look here
- Measured from the horizontal. The angle of elevation opens upward from the horizontal. Find that line first and the right triangle appears.
- Not here
- Measured from the vertical. Measuring from the tower gives 90° minus the real angle, and swaps sin and cos.
- What it teaches
- Every angle has a starting line. Find it before you measure.