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S4 Maths: Sine Rule and Cosine Rule (Paper 1 (basics))
S4 Maths: Sine Rule and Cosine Rule (Paper 1 (basics))
Paper 1 (basics): 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, A = 30 degrees, B = 45 degrees and a = 8 cm. Find b.
- FoundationTwo sides of a triangle are 5 cm and 7 cm with an included angle of 60 degrees. Find the third side.
- FoundationA triangle has sides 6 cm and 8 cm with an included angle of 30 degrees. Find its area.
- IntermediateIn triangle ABC, A = 40 degrees, B = 60 degrees and a = 10 cm. Find b.
- IntermediateTwo sides are 8 cm and 5 cm with an included angle of 120 degrees. Find the third side.
- IntermediateA triangle has sides 7 cm, 8 cm and 9 cm. Find the angle opposite the 9 cm side.
- ChallengeIn triangle ABC, a = 6 cm, A = 35 degrees and c = 9 cm. Find sin C and the two possible values of C.
- ChallengeA triangle has area 20 cm squared with two sides 8 cm and 6 cm. Find the two possible included angles.
- ChallengeA triangle has sides 5 cm, 6 cm and 9 cm. Find its largest angle.
- Error redoA student multiplies 8 by sin 30 degrees instead of dividing, getting 4 cm, given A = 30 degrees, B = 45 degrees and a = 8 cm. What is the correct b?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | b = 11.314 cm. | By the sine rule, b = 8 times sin 45 degrees divided by sin 30 degrees. |
| 2 | The third side is 6.245 cm. | By the cosine rule, c squared is 25 + 49 – 35, that is 39. |
| 3 | The area is 12 cm squared. | Area is 6 times 8 times sin 30 degrees, halved. |
| 4 | b = 13.473 cm. | b is 10 times sin 60 degrees divided by sin 40 degrees. |
| 5 | The third side is 11.358 cm. | The cosine of 120 degrees is -0.5, so c squared is 64 + 25 + 40, that is 129. |
| 6 | C = 73.398 degrees. | cos C is 32 over 112, which gives about 73.4 degrees. |
| 7 | sin C = 0.86, so C = 59.358 degrees or 120.642 degrees. | sin C is c sin A over a, and both angles stay legal when added to 35 degrees. |
| 8 | C = 56.443 degrees or 123.557 degrees. | sin C is 40 over 48, giving an acute and an obtuse answer. |
| 9 | The largest angle is 109.471 degrees. | The largest angle faces the 9 cm side, and cos C equals minus one third. |
| 10 | b = 11.314 cm. | The sine rule divides by sin A, so b is 8 times sin 45 degrees divided by sin 30 degrees. |
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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