Class 10 · Chapter 9

Some Applications of Trigonometry

Real-life problems on heights and distances using angles of elevation and depression.

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Tip: open the NCERT PDF for the original chapter text alongside the notes here.
Detailed theory
When you look up at an object above the horizontal, the angle between your line of sight and the horizontal is the angle of elevation. As the observer moves closer, the elevation increases; as they move away, it decreases.
Key concepts & formulas
01
Angle of elevation: angle from horizontal upward to an object.
02
Angle of depression: angle from horizontal downward to an object.
03
tan(elev)=heightbase\tan(\text{elev}) = \dfrac{\text{height}}{\text{base}}.
04
The angle is always measured from a horizontal line.
05
Same object seen from different points gives different angles.
06
tan30=1/3,  tan45=1,  tan60=3\tan 30 = 1/\sqrt 3,\; \tan 45 = 1,\; \tan 60 = \sqrt 3.
Gyaan Maths — CBSE Class 6-10, built for board-toppers.
v1.1 · Feb 2026