CBSE Math RevisionSome Applications of Trigonometry: CBSE Class 10 Maths knowledge organiser
Everything to know about some applications of trigonometry on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.
Key definitions
- Line of sight
- The line from the observer's eye to the object being looked at.
- Angle of elevation
- The angle above the horizontal to an object higher than the eye.
- Angle of depression
- The angle below the horizontal to an object lower than the eye.
Key formulas
| Height and distance | \(\tan\theta=\frac{\text{height}}{\text{horizontal distance}}\) |
| Angle of elevation (looking up) = angle of depression (looking down) between the same two points; use 30°, 45°, 60° |
Worked example
A 12 m ladder leans against a wall and makes \(60^\circ\) with the ground. How high up the wall does it reach?
\(\sin60^\circ=\dfrac{h}{12}\Rightarrow h=12\cdot\frac{\sqrt3}{2}=6\sqrt3\) m.
Common mistakes
- Measuring the angle of depression from the vertical instead of the horizontal.
- Forgetting the observer's eye height when a person's height is given.
- Using \(\sin\) when the hypotenuse is not involved. Pick the ratio from the two sides you actually have.
- Rounding \(\sqrt3\) too early. Keep surds until the last line.
You should be able to…
- Draw the right triangle for a height-and-distance problem and use tan, sin or cos with 30°, 45° and 60°.
- Solve angle-of-depression problems and the standard two-triangle problems where the observer moves.
- Write full-marks 5-mark answers with a labelled figure, two equations and a final answer with units.
- Handle mixed elevation-and-depression problems, moving objects and speed, and the unusual two-triangle set-ups.
The printable sheet
Revise it next
- Some Applications of Trigonometry: Class 10 notes
- Practise Some Applications of Trigonometry by step (Route to 95)
- Skill Builders
- CBSE Class 10 Maths formula sheet (PDF)
Other CBSE Class 10 Maths topics: Real Numbers · Polynomials · Pair of Linear Equations in Two Variables · Quadratic Equations · Arithmetic Progressions · Triangles · Coordinate Geometry · Introduction to Trigonometry · Circles · Areas Related to Circles · Surface Areas and Volumes · Statistics · Probability · All CBSE Class 10 Maths organisers