Trigonometry basics
Trigonometry basics · heights & distances
9 min read · Updated 2026-05-26
What is Trigonometry?
Trigonometry is the study of the ratios between the sides of a right-angled triangle — sine is opposite over hypotenuse, cosine adjacent over hypotenuse and tangent opposite over adjacent, remembered as SOH-CAH-TOA. CSAT needs the standard values at 0°, 30°, 45°, 60° and 90° and the identity sin²θ + cos²θ = 1. Height questions reduce to tan(angle) = height ÷ horizontal distance.
The story
A person stands 50 m from a tall building. The angle from his eyes to the top of the building is 60°. How tall is the building?
The tan trick: tan(60°) = height / 50. tan(60°) = √3 ≈ 1.732. Height = 50 × 1.732 = 86.6 m.
In 15 seconds, you've solved a Class 10 trigonometry problem.
Trigonometry on CSAT is rare but easy. Just 6 formulas, 1 table to memorise, and 80% of "heights and distances" problems become 30-second affairs.
Why this matters for UPSC
For CSAT (Paper II, qualifying 33%):
- 1-3 questions per paper are trigonometry. Heights & distances + basic identities.
- GS-I Geography: Cartography uses trig (latitude-longitude calculations).
- GS-III Science: Optics, surveying, navigation.
Modest weight in CSAT, but each question is fast if you know the table. 30 minutes of memorisation = ~3-5% of marks.