examreels Class 10 · Maths
Chapter 9

The complete Heights & Distances practice map

NCERT Class 10 Mathematics · Chapter 9 · Some Applications of Trigonometry

The two-triangle type is the one from the video you just watched. Chapter 9 has 22 questions, and they are three types. All three types, and the order to practise all 22 in, are on this page. Nothing is held back for later.

7 worked Examples + 15 Exercise 9.1 questions = 22

Take it with you

The Heights & Distances practice map — PDF

The same map, made to print: all 22 in order with their book pages, all 22 again in book order to look one up, the three types with what each one asks of you, and the counting sheet. Five sheets to keep beside your textbook.

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The three types

Every one of the 22 sits in exactly one type. The numbers below are the real member lists — not samples. Find the ones you have already done, and you can see what is left.

6

One triangle

6 of the 22
What it asks
Choose sin, cos or tan from the side you know and the side the question asks for.
What you need
Opposite · Adjacent · Hypotenuse, and the 30° · 45° · 60° table.
Example 1 Example 2 Ex 9.1 Q1 Q3 Q4 Q5

Video lesson: not made yet. This card and the PDF are what we have today.

4

Check the final answer

4 of the 22
What it asks
Does the triangle give the whole answer, or only one part of it?
What you need
Mark the part that sits outside the triangle. Then add it, subtract it, or take the distance difference.
Example 3 Ex 9.1 Q2 Q6 Q14

Video lesson: not made yet. This card and the PDF are what we have today.

12

Two triangles

12 of the 22
What it asks
How are the distances in the two triangles connected?
What you need
Same height · Same base · Longer base · Bases add · Distances subtract.
Example 4 Example 5 Example 6 Example 7 Ex 9.1 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q15

You just cracked this one.

The practice order · all 22

Practise in this order. It is built on what each question needs you to already know, so nothing asks you for a move you have not met yet. Open your textbook at the first one and work down.

Start here
  1. 01Ex 9.1 Q1 Circus artist, rope and poleBook page 141
One triangle
  1. 02Ex 9.1 Q4 Tower from 30 m awayBook page 141
  2. 03Ex 9.1 Q5 Kite and stringBook page 141
  3. 04Ex 9.1 Q3 Two playground slidesBook page 141
  4. 05Example 1 Tower from a point 15 m awayBook page 135
  5. 06Example 2 Ladder reaching a poleBook page 136
Check the final answer · part 1
  1. 07Example 3 Observer and chimneyBook page 137
  2. 08Ex 9.1 Q2 Broken treeBook page 141
Two triangles
  1. 09Example 4 Flagstaff on a buildingBook pages 137–138
  2. 10Ex 9.1 Q7 Tower above a buildingBook page 141
  3. 11Ex 9.1 Q8 Statue on a pedestalBook page 142
  4. 12Ex 9.1 Q9 Building and 50 m towerBook page 142
  5. 13Example 5 Tower with two shadow lengthsBook pages 138–139
  6. 14Ex 9.1 Q11 TV tower across a canalBook page 142
  7. 15Example 6 Two buildings and angles of depressionBook pages 139–140
  8. 16Ex 9.1 Q13 Lighthouse and two shipsBook page 142
  9. 17Example 7 Bridge and river banksBook pages 140–141
  10. 18Ex 9.1 Q10 Equal poles across a roadBook page 142
  11. 19Ex 9.1 Q12 Building and cable towerBook page 142
  12. 20Ex 9.1 Q15 Car approaching a towerBook pages 142–143
Check the final answer · part 2
  1. 21Ex 9.1 Q6 Boy walking toward a buildingBook page 141
  2. 22Ex 9.1 Q14 Girl and moving balloonBook page 142

Q6 and Q14 come last on purpose. Each one asks you to spot the part outside the triangle and to connect two triangles, both at once — so they are easier once each of those is familiar.

This is our practice order, worked out from what each question needs. It is not the order printed in your book, and it is not an official NCERT order.

Your book prints the exercise items as 1. to 15. We write them as Q1 to Q15 so a number never loses its exercise. Page numbers are the printed book pages of the 2026–27 reprint.

All 22 use only the 30°, 45° and 60° values.

What we counted

Two different things are counted here, and we keep them apart: the 22 questions in your textbook, and the Chapter 9 questions in the board papers we hold.

Across the 38 distinct Chapter 9 questions in the 41 board paper sets we admitted (four years), 27 use the two-triangle diagram.

Board papers we admitted · 4 years · 41 paper sets

Chapter 9 appears in all 41 of those paper sets.

Chapter 9 count · 41 of 41 paper sets
What we admitted, and how we counted
  • 41 CBSE board paper sets with their official marking schemes, across four sessions: 2022–23, 2023–24, 2024–25 and 2025–26.
  • The NCERT Class 10 Mathematics textbook, Chapter 9, 2026–27 reprint — the source of all 22 items and their page numbers. jemh109.pdf · SHA-256 89c6c125039bfb8c7708b6bc5a27321021de629d4a1608f7f94812a96698f63f
  • Those 41 sets print 66 Chapter 9 questions. Sets from the same session repeat questions between them, so after collapsing those repeats the count is 38 distinct questions, carrying 142 marks in total in those papers.
What we do not have, and what this does not say
  • We have no link from a board question to a textbook item. We never say that a board question is one of the 22, or that the 22 are what the board asks.
  • Official NCERT worked solutions are in our hands for Examples 1–7 only. For Exercise 9.1 Q1–Q15 we hold the printed questions, and the type each one belongs to here is our own reading of them, not an official solution.
  • 3 of the 38 come from merges we grade medium-confidence. Left unmerged, the count would read 43 distinct questions instead of 38.
  • Four sessions of papers, and nothing beyond them. None of this is a statement about a paper that has not been written yet.
  • The practice order is ours, derived from the 22 — not the book's printed order.

The videos

Honestly, where each one stands today. There is no button here, because there is nothing yet to open.

  • Two triangles the video that brought you here
  • One triangle video lesson not made yet
  • Check the final answer video lesson not made yet

When a type's video lesson is ready, it will be here. You do not have to wait for it to start: this page and the PDF carry the full map today — every type, every question number, and the order to practise them in.