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S3 Maths: Trigonometric Ratios (Paper 3 (challenge))
Tutor Prep Guide · Definitions of sine, cosine and tangent, finding ratios from the sides of a right-angled triangle, special angles 30, 45 and 60 degrees, and using ratios to recover sides, angles and angles of elevation
S3 Maths: Trigonometric Ratios (Paper 3 (challenge))
Paper 3 (challenge): ten questions on trigonometric ratios, with answers and notes.
Direct answers Level: S3 maths; format: definitions of ratios, special angles, finding sides and angles, angles of elevation.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S3 Maths: Trigonometric Ratios |
| Level | S3 |
02 Questions (10 items)
- FoundationA right-angled triangle has sides 7 cm, 24 cm and 25 cm. Find the sine of the angle facing the shortest side.
- FoundationFor the same 7, 24, 25 triangle, find the cosine of that angle.
- FoundationFor the same 7, 24, 25 triangle, find the tangent of that angle.
- IntermediateIn a right-angled triangle the opposite side is 3 cm and the adjacent side is 4 cm. Find angle A to one decimal place.
- IntermediateFrom a point 50 m from the foot of a tower the angle of elevation of the top is 30 degrees. Find the height to one decimal place.
- IntermediateA right-angled triangle has sides 20 cm, 21 cm and 29 cm. Find the tangent of the angle facing the shortest side.
- ChallengeA ramp is 20 m long and rises 8 m. Find the angle it makes with the horizontal, to one decimal place.
- ChallengeAngle A is acute and sin A is 0.5. Find A and its tangent to three decimal places.
- ChallengeA flagpole 12 m high casts a 20 m shadow. Find the angle of elevation of the sun to one decimal place.
- Error redoError clinic: a student answers that tan 60 degrees equals 60. What is the correct value to three decimal places?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 7/25 (that is 0.28) | With an opposite side of 7 cm and hypotenuse 25 cm the sine is 7 over 25, which is 0.28. |
| 2 | 24/25 (that is 0.96) | With an adjacent side of 24 cm and hypotenuse 25 cm the cosine is 24 over 25, which is 0.96. |
| 3 | 7/24 (that is 0.292) | Tangent is 7 cm over 24 cm, which is about 0.292. |
| 4 | 36.9° | The tangent is 0.75, so the inverse tangent gives about 36.9 degrees. |
| 5 | 28.9 m | The height equals the horizontal distance times the tangent, so 50 times 0.577 is about 28.9 m. |
| 6 | 20/21 (that is 0.952) | With opposite 20 cm and adjacent 21 cm the tangent is 20 over 21, about 0.952. |
| 7 | 23.6° | The sine is 8 over 20, namely 0.4, so the angle is about 23.6 degrees. |
| 8 | 30 degrees; tan A is 0.577 | A sine of 0.5 corresponds to 30 degrees, whose tangent is 0.577. |
| 9 | 31° | The tangent is 12 over 20, namely 0.6, so the angle is about 31.0 degrees. |
| 10 | 1.732 | Tangent is a ratio of sides, not the angle itself; tan 60 degrees is the square root of three, about 1.732. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Identify the opposite, adjacent and hypotenuse sides first, then choose the ratio. The hypotenuse appears only in sine and cosine, while tangent uses opposite over adjacent.Tutor Registration →
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.
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