SSC CGL Tier 2 Trigonometry & Geometry: Formulas + Practice Questions

Trigonometry and advanced Geometry are the two biggest new topics Tier 2 introduces that Tier 1 doesn't test at all. If you've cleared Tier 1 without ever touching these, this is where to start. Note: unlike our Tier 1 content, we don't have a verified Tier 2 real-PYQ dataset yet, so the practice questions below are original problems built directly from the official syllabus topics — not claimed as extracted exam questions.

Trigonometry: Core Ratios

Everything in Tier 2 Trigonometry builds from these six ratios, defined for a right-angled triangle:

• sin θ = Opposite / Hypotenuse
• cos θ = Adjacent / Hypotenuse
• tan θ = Opposite / Adjacent = sin θ / cos θ
• cosec θ = 1 / sin θ
• sec θ = 1 / cos θ
• cot θ = 1 / tan θ

Standard Angle Values (Memorize These)

θ	0°	30°	45°	60°	90°
sin θ	0	1/2	1/√2	√3/2	1
cos θ	1	√3/2	1/√2	1/2	0
tan θ	0	1/√3	1	√3	Not defined

Key Trigonometric Identities

• sin²θ + cos²θ = 1
• 1 + tan²θ = sec²θ
• 1 + cot²θ = cosec²θ

Worked Example 1: Basic Identity Application

Q: If sin θ = 3/5, find cos θ and tan θ (θ acute).

Solution: Using sin²θ + cos²θ = 1: cos²θ = 1 − 9/25 = 16/25, so cos θ = 4/5. Then tan θ = sin θ / cos θ = (3/5)/(4/5) = 3/4.

Heights & Distances: The Most Common Question Type

This is the practical application of Trigonometry that appears most often — using angles of elevation/depression to find heights or distances.

Worked Example 2: Height & Distance

Q: A tower's shadow is 30 m long when the sun's angle of elevation is 30°. Find the height of the tower.

Solution: tan 30° = Height / Shadow length. So Height = 30 × tan 30° = 30 × (1/√3) = 30/√3 = 10√3 ≈ 17.32 m.

Worked Example 3: Angle of Depression

Q: From the top of a 60 m tall building, the angle of depression to a car on the ground is 45°. Find the distance from the base of the building to the car.

Solution: The angle of depression equals the angle of elevation from the car's position (alternate angles). tan 45° = Height / Distance → 1 = 60 / Distance → Distance = 60 m.

Geometry: Key Formulas for Tier 2

Shape	Area	Perimeter / Circumference
Circle	πr²	2πr
Triangle	½ × base × height	Sum of all sides
Equilateral Triangle	(√3/4) × side²	3 × side
Rectangle	length × breadth	2(length + breadth)
Trapezium	½ × (sum of parallel sides) × height	Sum of all sides

Circle Theorems Worth Memorizing

• The angle subtended by an arc at the center is twice the angle subtended at any point on the remaining circumference
• Angles in the same segment of a circle are equal
• The angle in a semicircle is always 90°
• Tangent to a circle is perpendicular to the radius at the point of contact

Worked Example 4: Circle Theorem Application

Q: A triangle is inscribed in a circle such that one side is the diameter. If one of the other angles is 35°, find the third angle.

Solution: Since one side is the diameter, the angle opposite to it (the angle in the semicircle) is 90°. So the third angle = 180° − 90° − 35° = 55°.

Worked Example 5: Mensuration Combination

Q: Find the area of an equilateral triangle with side 8 cm.

Solution: Area = (√3/4) × 8² = (√3/4) × 64 = 16√3 ≈ 27.7 cm².

How to Study This Efficiently

• Memorize the standard angle table cold — most Trigonometry questions build directly on recalling these instantly rather than deriving them each time
• Practice heights-and-distances problems by always drawing the triangle first — visualizing the right angle, the given angle, and what you're solving for prevents setup errors
• For Geometry, memorize the circle theorems as rules, not proofs — Tier 2 tests application speed, not derivation
• Build a single-page formula sheet combining this article's tables and revisit it daily during your Tier 2 prep phase

Frequently Asked Questions

Q1. How much of Tier 2 Quant is Trigonometry and Geometry combined?
These typically make up a meaningful portion of the Mathematical Abilities section, though exact proportions vary by paper — treat them as core topics, not optional extras, since they don't appear in Tier 1 at all and can't be skipped.

Q2. Do I need to memorize proofs for circle theorems?
No — Tier 2 tests your ability to apply these theorems quickly to solve problems, not to derive or prove them from scratch.

Q3. Is this content based on real Tier 2 PYQs?
Not yet — these are original practice problems built directly from the official Tier 2 syllabus topics. We don't currently have a verified real Tier 2 PYQ dataset the way we do for Tier 1; this will be flagged clearly if that changes in future articles.

For the complete Tier 2 syllabus overview, see our Tier 2 Syllabus & Exam Pattern article, and our Tier 2 Preparation Strategy guide for how to adjust your overall approach.