Geometry & Trigonometry — RRB NTPC Mathematics
This topic carries roughly 6% of Mathematics's 30 questions. The geometry half tests standard angle properties (triangle angle sum, exterior angle, polygon interior angles); the trigonometry half stays limited to the standard-angle table applied to simple height-and-distance word problems.
1. What RRB NTPC actually asks
Expect triangle angle-sum problems, the exterior angle theorem, polygon interior-angle-sum problems, Pythagorean-triple-based right-triangle problems, standard trigonometric ratio values (sin, cos, tan at 30°, 45°, 60°), and heights-and-distances word problems using a single angle of elevation.
2. Core angle properties
- Sum of interior angles of a triangle = 180°.
- Exterior angle theorem: an exterior angle of a triangle equals the sum of the two non-adjacent (opposite) interior angles.
- Sum of interior angles of a polygon with n sides = (n−2) × 180°.
- Angle subtended by an arc: the angle at the centre of a circle is twice the angle subtended by the same arc at any point on the circumference.
3. The standard trigonometric ratio table
| Angle | sin | cos | tan |
|---|---|---|---|
| 30° | 1/2 | √3/2 | 1/√3 |
| 45° | 1/√2 | 1/√2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
This table should be memorised cold — nearly every trigonometry question at this level substitutes directly from it.
4. Heights and distances
For a single angle of elevation θ from a point at horizontal distance d from the base of a tower/pole of height h: tan θ = h/d, so h = d × tan θ. This is the only trigonometric relationship needed for RRB NTPC's heights-and-distances questions.
Worked examples
Q1. Two angles of a triangle measure 50° and 70°. What is the third angle?
Pick an option to check your answer.
Show explanation
Solution. The three angles of a triangle sum to 180°. Third angle = 180 − 50 − 70 = 60°. Answer: (c).
Q2. A tower casts an observation such that the angle of elevation from a point 20 m away from its base is 60°. What is the height of the tower?
Pick an option to check your answer.
Show explanation
Solution. Using tan θ = h/d with θ = 60° and d = 20: h = 20 × tan 60° = 20 × √3 = 20√3 m.
A common error is using tan 30° instead of tan 60° (confusing which trig ratio corresponds to the given angle), or forgetting to multiply by the distance entirely. Answer: (b).
6. Common traps
- Confusing the exterior angle theorem's direction. The exterior angle equals the sum of the two OPPOSITE (non-adjacent) interior angles, not the adjacent one.
- Misreading the polygon interior-angle-sum formula. It's (n−2)×180°, not n×180° — always subtract 2 from the number of sides first.
- Mixing up sin, cos, and tan values from the standard table — a quick way to catch this is remembering sin and cos values are mirror images between 30° and 60° (sin30°=cos60°=1/2, and sin60°=cos30°=√3/2).
- Using the wrong angle in a heights-and-distances problem when two elevation angles or two candidate angles are given — always match tan θ to the specific angle stated for that particular distance.
7. Guessing strategy
For heights-and-distances questions, a quick check of which trig value (1/2, 1/√2, or √3) an option corresponds to is often enough to eliminate options that clearly used the wrong angle's ratio.
Summary
- Geometry & Trigonometry is roughly 6% of Mathematics's 30 CBT 1 questions.
- Triangle angle sum = 180°; polygon interior angle sum = (n−2)×180°; exterior angle = sum of the two opposite interior angles.
- Memorise the standard trig ratio table for 30°, 45°, and 60° cold.
- Heights and distances at this level use only tan θ = h/d, so h = d × tan θ.
- The exterior angle theorem uses the two OPPOSITE interior angles, not the adjacent one.
- sin and cos values mirror between 30° and 60° — a useful memory check.
