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S3 Maths: Trigonometric Ratios (Paper 2 (intermediate))
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 2 (intermediate))
Paper 2 (intermediate): 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 8 cm, 15 cm and 17 cm. Find the sine of the angle facing the shortest side.
- FoundationFor the same 8, 15, 17 triangle, find the cosine of that angle.
- FoundationFor the same 8, 15, 17 triangle, find the tangent of that angle.
- IntermediateIn a right-angled triangle the hypotenuse is 25 cm and sin A is 3 over 5. Find the opposite side.
- IntermediateUsing the same triangle, find the adjacent side by Pythagoras theorem.
- IntermediateFind the value of tan 30 degrees, correct to three decimal places.
- ChallengeGiven tan A is 3 over 4 and the opposite side is 9 cm, find the adjacent side.
- ChallengeFind the value of sin 45 degrees, correct to three decimal places.
- ChallengeA right-angled triangle has hypotenuse 26 cm and opposite side 10 cm. Find the adjacent side.
- Error redoError clinic: a student uses sine to find an adjacent side. Which ratio should be used?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 8/17 (that is 0.471) | The shortest side of 8 cm is opposite that angle and the hypotenuse is 17 cm, so the sine is 8 over 17. |
| 2 | 15/17 (that is 0.882) | The adjacent side is 15 cm and the hypotenuse is 17 cm, so the cosine is 15 over 17. |
| 3 | 8/15 (that is 0.533) | Tangent is 8 cm over 15 cm, so the value is 8 over 15. |
| 4 | 15 cm | The opposite side equals the hypotenuse times the sine, so 25 times 3 over 5 gives 15 cm. |
| 5 | 20 cm | The square of the adjacent side is 625 minus 225, which is 400, so the side is 20 cm. |
| 6 | 0.577 | The tangent of 30 degrees is one over the square root of three, which is 0.577 to three decimal places. |
| 7 | 12 cm | The adjacent side is the opposite side divided by the tangent, so 9 times 4 over 3 gives 12 cm. |
| 8 | 0.707 | At 45 degrees the two legs are equal, so the sine is one over the square root of two, which is 0.707. |
| 9 | 24 cm | The square of the adjacent side is 676 minus 100, which is 576, so the side is 24 cm. |
| 10 | cosine | The ratio of the adjacent side to the hypotenuse is the cosine, so cosine is the right choice. |
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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