Height and Distance Tests — Pick a Level and Start
Tap a level to see every test in it. Level 1 is set at real SSC CGL difficulty — start there the day you finish the concept. Level 2 is pitched above the exam, to push accuracy under pressure.
Level 1 SSC CGL Level Checking… View tests
Same difficulty as the real SSC CGL paper — one triangle, or two that share a side, with 30°, 45° and 60°. A height from a distance and a distance from a height; the length of a string, rope or wire; a walk towards a tower that turns two angles into a height; two cars, boats or jeeps on the same side or on opposite sides; equal lamp posts across a road; a flagstaff, statue or hoarding on a building; the elevation of a tower's top and the depression of its foot from a rooftop; depressions from a hill; two buildings across a street; shadows at the same moment and the sun's altitude; complementary angles; the 15°–30° and 30°–60° isosceles tricks; broken trees; ladders; a cloud and its reflection; a line of sight through a tree to a building; and ships due north and due east. A steady score here means the chapter is exam-ready.
Level 2 Above SSC CGL Level Checking… View tests
Harder than the exam asks, because every question chains two steps or runs one backwards. Angles of 15° and 75° with tan 15° = 2 − √3; angles given only as a tangent or a sine; the tan 2θ formula for a statue and its pedestal that look equally tall; two positions between towers where the angles are complementary; a building's height found from one sighting and used for the next; an eye height that cancels out; a shadow that climbs a wall; a balloon seen by two observers at once; a kite on the same string in a changed wind; speed in km/h turned into a height; the time left for an approaching boat; a ship that sails east after being sighted due north; and letter-form answers in terms of h. Clear these and the real paper feels easy.
A height and distance question is one right triangle drawn from a sentence. The tower is the vertical side, the ground is the horizontal side, and the line of sight is the slant. Whatever the story — a lighthouse, a kite, a balloon, a flagstaff — the working is the same line: tan of the angle = height ÷ horizontal distance. Everything else is deciding which height and which distance belong to that angle.
The marks are lost in three places. The first is measuring from the wrong level — from a rooftop or an observer's eye, only the part of the tower above that level belongs to the triangle, and the rest must be added back. The second is adding when you should subtract: two points on the same side of a tower are a difference of distances, two points on opposite sides a sum. The third is multiplying by tan when you should divide — height = distance × tan θ, but distance = height ÷ tan θ. Each test puts twenty-five height and distance questions in front of you in one sitting, which is what makes those checks automatic.
How Many Height and Distance Questions Are Asked in SSC CGL?
Heights and distances turns up in most shifts, usually as one question in Tier I and one or two in Tier II. It is the most direct use of trigonometry in the paper, and with the standard values ready it is quick marks.
| Chapter | Tier I (out of 25) | Tier II Paper I (out of 30) |
|---|---|---|
| Heights & Distances | 0–1 | 1–2 |
| Trigonometry (identities & values) | 1–2 | 2–3 |
Counts vary by shift. Height and distance questions use only the trigonometric ratios of standard angles, so the two chapters are best prepared together.
What You Will Practice in the Height and Distance Chapter
One observer, one triangle
- A height from a distance and an angle, and a distance from a height and an angle
- Depression from a window or a rooftop turned into a ground distance
- An observer's eye height added to the triangle
- Strings, ropes, cables and wires — length from height, height from length, the peg's distance
- The angle itself, from a height-to-distance ratio or a wire length
- Angles given as a tangent or a sine instead of in degrees
Two observers, two positions, two objects
- Walking towards a tower — the height from two angles, or the distance walked
- Two cars, boats or people on the same side (a difference) or on opposite sides (a sum)
- Equal poles on either side of a road, and unequal towers with a point between them
- A flagstaff, statue, poster or hoarding on top of a building
- From a rooftop: the elevation of a tower's top and the depression of its foot
- From a hill: the depressions of the top and the foot of a shorter tower
- Two buildings across a street, and a rope or cable joining two tops
- Raising a tower until its top is seen at a steeper angle
Special set-ups
- Shadows at the same moment, and shadows as the sun's altitude changes
- Complementary angles (h = √(ab)) and the midpoint of two pillars
- Angle doubling — 15° and 30°, 30° and 60°, θ and 2θ
- Broken trees and ladders that slip, slide or turn across a street
- A cloud and its reflection in a lake
- A line of sight through the top of a tree to the top of a building
- Poles in a triangular park seen at equal angles from every corner
- Objects due north and due east of a tower
- Speed or time from a change of angle — aeroplanes, cars, boats and balloons
Rules worth memorising
| Situation | Rule |
|---|---|
| Standard values | tan 30° = 1/√3, tan 45° = 1, tan 60° = √3 |
| 15° and 75° | tan 15° = 2 − √3, tan 75° = 2 + √3; their product is 1 |
| Height and distance | h = d tan θ, d = h ÷ tan θ |
| String, wire or ladder of length L | height = L sin θ, ground distance = L cos θ |
| Two points, same side | gap = h(cot α − cot β) |
| Two points, opposite sides | gap = h(cot α + cot β) |
| Walk d, angle 30° → 60° | h = d√3 ÷ 2; slant from the nearer point = d |
| Complementary angles from a and b | h = √(ab) |
| Object of length f on a building | f = d(tan β − tan α); at 30° and 60° the whole is 3 × the building |
| From a rooftop of height b | tower = b + d tan(elevation), with d = b ÷ tan(depression) |
| Shadow at altitude θ | shadow = h ÷ tan θ; at one moment, height ÷ shadow is the same for every object |
| Cloud and reflection from height h | cloud height = h(tan β + tan α) ÷ (tan β − tan α) |
| Due north and due east | gap = √(d1² + d2²), each d = h ÷ tan θ |
| Approaching, 30° → 60° in t | time still needed to reach the foot = t ÷ 2 |
The third row carries almost the whole chapter. Most other rules are that one line applied twice and then added or subtracted.
The three mistakes that cost the most marks
- Measuring from the ground when the eye is higher. From a rooftop, a window or an observer's eye, the triangle starts at that level. Find the part above it, then add the height below.
- Sum and difference swapped. Two points on the same side of a tower give a difference of distances; on opposite sides, a sum. Draw the foot of the tower before you write anything.
- Multiplying by tan when you should divide. A steep angle means a tall height and a short distance. If your answer makes a 60° sighting look farther than it is high, you have divided the wrong way.
Solved Examples — SSC CGL Height and Distance Questions
tan θ = height ÷ distance. So h = 30 × tan 60° = 30√3 ≈ 51.96 m. A steep angle gives a height greater than the distance, which checks out. Answer: 30√3 mh√3 and h ÷ √3, and their difference is 40: 2h ÷ √3 = 40, so h = 20√3 m. Shortcut: for 30° to 60°, h = d√3 ÷ 2. Answer: 20√3 md = 60 ÷ tan 60° = 20√3 m. The drop to the tower's top is d tan 30° = 20 m, so the tower is 60 − 20 = 40 m. Answer: 40 mh/4 and h/9 multiply to 1. Then h² = 36 and h = 6 m. The rule h = √(ab) holds whether the points are on the same side or on opposite sides. Answer: 6 mHow the Height and Distance Chapter Tests Work
- 25 questions per test, with a full question palette — answered, skipped, marked for review, not visited.
- Optional 15-minute timer — with the clock to build exam speed, without it while you are still learning the chapter.
- Marking: +2 correct, −0.5 wrong, 0 unattempted — the same scheme as the real paper.
- Solutions, shortcut tricks and concept notes open after you submit, question by question.
- English and हिंदी, chosen at the start of every test.
- Free with a TrickySSC account — sign in once with Google or your mobile number, and every test is open to you.
How to Prepare Heights and Distances for SSC CGL
- Know five tangents cold. 30°, 45°, 60°, and for harder papers 15° and 75°. Almost every question is one of these.
- Draw the figure every time. A rough sketch with the tower, the ground and the line of sight settles which side is which before any numbers go in.
- Mark the eye level. From a rooftop, a window or a person's eyes, draw the horizontal first; only the part of the tower above it belongs to the angle.
- Say “same side” or “opposite sides” out loud. Same side subtracts the distances; opposite sides adds them.
- Use the angle of depression as an angle of elevation. The two are equal (alternate angles), so every depression question becomes an ordinary triangle from below.
- Learn the three ready-made answers. 30° to 60° over a walk d gives
d√3 ÷ 2; complementary angles give√(ab); 30° and 60° from one point make the whole three times the lower part. - Rationalise at the end. Keep answers like
20 ÷ (√3 − 1)until the last step, then multiply by√3 + 1to match the options. - Check the size of the answer. Below 45° the distance is more than the height; above 45° it is less. One glance rules out two options.
- Do Level 1 untimed, the same day you finish the theory. It is set at real SSC CGL difficulty; the aim is picking the right triangle, not speed.
- Repeat Level 1 with the 15-minute clock on, then move to Level 2. After that, verify against a previous year paper and a full mock test under locked sectional timing.
All SSC CGL Chapter Wise Tests
Every chapter below has its own free Level 1 and Level 2 tests with full solutions.
Browse all 45 chapter tests — Maths (35) · Reasoning (10)
- Number System
- Rule of Divisibility
- Remainder Theorem
- Decimal & Fraction
- LCM & HCF
- Square & Cube Root
- Number Series (AP & GP)
- Power, Indices & Surds
- Algebraic Formula
- Algebraic Result
- Algebraic Expression & Identities
- Percentage
- Profit & Loss
- Discount & Marked Price
- Simple Interest
- Compound Interest
- Ratio & Proportion
- Partnership
- Average
- Problems on Ages
- Mixture & Alligation
- Time & Work
- Pipe and Cistern
- Time, Speed and Distance
- Quadratic Equation
- Boat and Stream
- Races
- Trigonometry
- Heights & Distances
- Geometry
- Mensuration
- Coordinate Geometry
- Probability
- Statistics
- Data Interpretation
- All Maths chapters →
SSC CGL ऊँचाई और दूरी (Height and Distance) चैप्टर टेस्ट — हिंदी में
ऊँचाई और दूरी का हर प्रश्न एक समकोण त्रिभुज है: मीनार ऊर्ध्वाधर भुजा, ज़मीन क्षैतिज भुजा और दृष्टि-रेखा कर्ण। पूरा अध्याय एक ही पंक्ति पर टिका है: कोण का tan = ऊँचाई ÷ क्षैतिज दूरी। उन्नयन कोण (ANGLE OF ELEVATION) ऊपर देखने पर और अवनमन कोण (ANGLE OF DEPRESSION) नीचे देखने पर बनता है — और दोनों बराबर होते हैं।
अंक तीन जगह कटते हैं। पहली: छत या आँख की ऊँचाई भूल जाना — छत से देखने पर त्रिभुज उसी स्तर से शुरू होता है, नीचे का भाग अलग से जोड़ना पड़ता है। दूसरी: एक ही ओर और विपरीत ओर को उलट देना — एक ही ओर दूरियाँ घटती हैं, विपरीत ओर जुड़ती हैं। तीसरी: tan से गुणा की जगह भाग (या उलटा) — ऊँचाई = दूरी × tan θ, दूरी = ऊँचाई ÷ tan θ।
TrickySSC पर इस अध्याय के सभी टेस्ट हिंदी में उपलब्ध हैं — प्रश्न, विकल्प, विस्तृत हल और शॉर्टकट ट्रिक सब हिंदी में। दो स्तर हैं: लेवल 1 (SSC CGL के स्तर का) और लेवल 2 (SSC CGL से कठिन)। प्रत्येक टेस्ट में 25 प्रश्न, वैकल्पिक 15 मिनट का टाइमर और +2 / −0.5 की वही मार्किंग जो असली परीक्षा में होती है।