CDS Mathematics · Teaching notes
Heights and Distances — CDS Elementary Mathematics
Heights and Distances has 41 past-year questions in CDS Elementary Mathematics, in 19 of the twenty-one sittings from 2016 (II) to 2026 (II). Fourteen of them are HARD, a larger share than in most chapters, and two observation points account for 19: every problem is one or two right triangles sharing a height or a ground distance. The pages go from a single line of sight to two observation points, an observer above the ground, and towers standing on plane figures.
Every subtopic, worked example, formula and trap in one printable document — answers shown, ready to share.
Subtopic notes
One Line of Sight
6 PYQsA height, a ground distance and a line of sight make one right triangle; the angle of elevation links the two legs by its tangent.
Two Points of Observation
19 PYQsTwo observations of one height give two ground distances, h cot α and h cot β; the question hands you their difference or their sum.
Observer Above the Ground
9 PYQsAn observer above the ground sees the top of a taller object by elevation and its foot by depression; the level line through the eye splits the object in two.
Towers on Plane Figures and Bearings
7 PYQsWhen towers stand at the corners or centre of a square, rectangle or hexagon, the ground distances come from the plane figure, and each tower is its own right triangle.
Formula & revision sheet
5 formulas · 6 gotchas across all subtopics — the exam-eve cheat-sheet
Formula & revision sheet
5 formulas · 6 gotchas across all subtopics — the exam-eve cheat-sheet
Formulas (1)
Watch out for (1)
- Is the given length slant or level?→ Height, distance and the angle
Formulas (2)
Watch out for (3)
- Same side or opposite sides?→ Difference and sum of the distances
- Nearer point, larger angle→ Difference and sum of the distances
- Heights multiply, distances multiply→ Complementary angles
Watch out for (1)
- Add the part below eye level→ Elevation and depression together
Watch out for (1)
- Which diagonal of the hexagon?→ Ground distances from the figure
PYQ weightage by concept
5 concepts · 41 PYQs — where the marks actually sit, so you know what to drill first
PYQ weightage by concept
5 concepts · 41 PYQs — where the marks actually sit, so you know what to drill first
| Concept | PYQs | Share |
|---|---|---|
| Difference and sum of the distances | 14 | 34% |
| Complementary angles | 5 | 12% |
| Concept | PYQs | Share |
|---|---|---|
| Ground distances from the figure | 7 | 17% |
Test yourself on Heights and Distances
15 past CDS questions from this chapter, timed at 18 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.