NCERT Mathematics, Class 10, textbook pages 133–143

How to help your child with Class 10 Maths Chapter 9, Some Applications of Trigonometry, at home

Heights and distances, explained for parents: a 45-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

θdistanceheightheight = distance × tan θ

NCERT Class 10 Maths Chapter 9 Some Applications of Trigonometry: what it teaches

Your teen uses angles of elevation and depression with trigonometric ratios to find heights of buildings, widths of rivers and distances that can’t be measured directly.

Why it matters later. Applications of trigonometry are used in physics, surveying and navigation.

See it: this chapter in pictures

20 m away, elevation 45°height = 20 × tan 45°= 20 m (+ eye height)
Include the observer’s eye height.
depressioncar
Depression is measured down from the horizontal.
clinometer: protractor + straw+ thread and weightmeasure real angles
Measure real heights at home.

You need

  • a clinometer (protractor, straw and thread)
  • a measuring tape

Tonight’s 45 minutes

  1. Make a clinometer and measure the angle of elevation to a building top from a known distance.
  2. Calculate the height: height = distance × tan θ (+ eye height).
  3. Draw a diagram for an angle of depression problem from a balcony.
  4. Solve a two-angle problem (moving closer to a tower).

Words to use

  • angle of elevation
  • angle of depression
  • line of sight
  • horizontal
  • tan

Watch for

  • Measuring elevation from the vertical. Angles are measured from the horizontal.
  • Forgetting observer’s eye height. Add it to the calculated height.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouElevation 45° from 20 m. Height?

Your childtan 45° = 1, so 20 m plus eye height.

A game for this week: Height hunt

  1. Make a clinometer.
  2. Measure elevations of three tall objects.
  3. Calculate heights.
  4. Compare with estimates.

A 5-day plan, 45 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Surveying land.
  • Tree and building heights.
  • Aircraft landing angles.
  • Lighthouse distances.

Quick check

Ask these at the end of the week. Tap to see the answer.

From 20 m away, elevation 45°. Height above eye level?

20 m.

Angle of depression equals which angle?

The angle of elevation from the other point (alternate angles).

tan 60° = √3. From 10 m, height?

10√3 ≈ 17.3 m.

Ready for the next chapter when your child…

  • Draws correct diagrams.
  • Uses tan, sin, cos for heights.
  • Includes observer height.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 10). See the full Class 10 parent guide for every chapter.

Questions parents ask

What is an angle of elevation?

The angle above the horizontal to an object.

How do I start these problems?

Draw a clear right triangle diagram with the known values.

Can I use a phone to measure angles?

Yes, many phones have angle apps.