Playbook
Heights and Distances
41 q · 34% HARD · about two a paper. Towers on plane figures is 5 of 7 HARD; one line of sight and two points of observation are the pages to bank.
- Questions in the bank
- 41
- q/paper (21 papers)
- 1.95
- Tagged HARD
- 34%
- Subtopics
- 4
Strand: Selective
When you’ll see it
An angle of elevation or depression and a height or distance to find.
How this chapter is tested
41 questions, about two a paper, at 34% HARD, the second-highest in the bank. Towers on plane figures (5 of 7 HARD) is the pool; one line of sight and two points of observation are the pages to bank.
Every question is one or two right triangles sharing a height or a ground distance. Standard angles (30°, 45°, 60°) make the tangents exact.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
One line of sight
height = distance × tan θ.
Two observation points
Same side: subtract the distances; opposite sides: add them.
Observer above the ground
Split the object at the observer's eye level into two triangles.
Towers on plane figures
The ground distances come from the figure (a square's diagonal, a hexagon's side).
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.
Complementary angles
Elevations α and 90° − α from distances a and b give height √(ab).
Depression equals elevation
The angle of depression from A to B equals the angle of elevation from B to A.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each subtopic. Read the notes once, then drill subtopic by subtopic below.
Heights and Distances notesDrill every Heights and Distances question
41 questions from the bank, across 4 subtopics.
Drill one subtopic at a time
The 4 subtopics, in teaching order.
- One Line of SightDrill One Line of Sight
- Two Points of ObservationDrill Two Points of Observation
- Observer Above the GroundDrill Observer Above the Ground
- Towers on Plane Figures and BearingsDrill Towers on Plane Figures and Bearings
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