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S4 Maths: Sine Rule and Cosine Rule (Paper 2 (intermediate))
S4 Maths: Sine Rule and Cosine Rule (Paper 2 (intermediate))
Paper 2 (intermediate): ten questions on the sine rule and the cosine rule with answers and one-line notes.
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: S4 Maths: Sine Rule and Cosine Rule |
| Level | S4 |
02 Questions (10 items)
- FoundationIn triangle ABC, B = 50 degrees, C = 70 degrees and b = 12 cm. Find c.
- FoundationTwo sides are 9 cm and 11 cm with an included angle of 45 degrees. Find the third side.
- FoundationA triangle has sides 10 cm and 14 cm with an included angle of 40 degrees. Find its area.
- IntermediateA triangle has sides 7 cm, 9 cm and 12 cm. Find the angle opposite the 7 cm side.
- IntermediateIn triangle ABC, b = 15 cm, B = 35 degrees and A = 80 degrees. Find a.
- IntermediateA triangle has sides 7 cm, 8 cm and 9 cm. Find its area.
- ChallengeIn triangle ABC, a = 8 cm, b = 10 cm and A = 30 degrees. Find all possible values of B and say whether both are valid.
- ChallengeA triangle has sides 5 cm, 12 cm and 13 cm. Find the angle opposite the 13 cm side.
- ChallengeA triangle has area 30 cm squared with sides 10 cm and 12 cm. Find the two possible included angles.
- Error redoA student writes c squared = 36 + 64 + 96 times cos 60 degrees and gets 12.166 cm for sides 6 and 8 with included angle 60 degrees. What is the correct c?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | c = 14.72 cm. | c is 12 times sin 70 degrees divided by sin 50 degrees. |
| 2 | The third side is 7.874 cm. | c squared is 81 + 121 minus 198 times cos 45 degrees, about 62. |
| 3 | The area is 44.995 cm squared. | Area is 10 times 14 times sin 40 degrees, halved. |
| 4 | A = 35.431 degrees. | cos A is (81 + 144 – 49) over 216. |
| 5 | a = 25.754 cm. | a is 15 times sin 80 degrees divided by sin 35 degrees. |
| 6 | The area is 26.833 cm squared. | With s = 12 the area is the square root of 12 times 5 times 4 times 3. |
| 7 | B = 38.682 degrees or 141.318 degrees, and both are valid. | sin B is 0.625, and 30 plus 141.3 is still under 180, so two triangles fit. |
| 8 | C = 90 degrees, a right angle. | cos C is (25 + 144 – 169) over 120, which is 0. |
| 9 | A = 30 degrees or 150 degrees. | sin A is 60 over 120, so A is 30 or 150 degrees. |
| 10 | c = 7.211 cm. | The cosine rule subtracts 2ab cos C, so c squared is 36 + 64 – 48, that is 52. |
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.
Ask what you hold first: three sides, two sides with the included angle, or two angles with a side. Use the sine rule for two angles and a side, and the cosine rule when the included angle is known. When a sine rule gives an angle, check whether 180 degrees minus it is still valid, because that gives a second triangle. For the area, take half the product of two sides times the sine of the included angle.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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