Free Sine & cosine rules questions for IGCSE Mathematics (0580), Extended tier (Supplement content), part of Trigonometry. Each question has the answer and the marking points an examiner would look for.
Generate a full Sine & Cosine Rules worksheet →All Trigonometry questionsThe diagram shows a cuboid ABCDEFGH.
Calculate the length of the diagonal AG.
Calculate the angle between AG and the base ABCD.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 19.8 cm AC2 = 152 + 52 M1 AG2 = 152 + 52 + 122 M1 19.8 A1 | 3 |
| (b) | 37.2° angle GAC identified B1 tan = 1215.81 or sin = 1219.85 M1 37.2 A1 | 3 |
A boat sails 12 km from A to B on a bearing of 040°. It then sails 9 km from B to C on a bearing of 125°.
Show that angle ABC = 95°.
Calculate the distance AC.
Calculate the bearing on which the boat must sail to return directly from C to A.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 95° uses co-interior / bearing of A from B = 220 M1 220 − 125 = 95 A1 | 2 |
| (b) | 15.6 km cosine rule M1 AC² = 12² + 9² − 2 × 12 × 9 × cos 95° M1 15.6 km A1 | 3 |
| (c) | 255° sine rule for angle BAC M1 angle BAC = 35.0° A1 255° A1 | 3 |
The diagram shows triangle ABC.
Calculate the length of AC.
| Part | Answer and marking points | Marks |
|---|---|---|
| 23.6 cm ACsin 63 = 17sin 40 M2 M1 for a correct implicit sine rule 23.6 A1 | 3 |
In triangle ABC, AB = 15 cm, AC = 14 cm and angle BAC = 108°.
Calculate BC.
Calculate angle ABC.
Calculate the shortest distance from C to the line AB.
Calculate the area of triangle ABC.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 23.5 cm BC2 = 142 + 152 − 2 × 14 × 15 × cos 108 M2 23.5 A1 | 3 |
| (b) | 34.6° sin B14 = sin 10823.47 M2 34.6 A1 | 3 |
| (c) | 13.3 cm 14 sin 108 M1 13.3 A1 | 2 |
| (d) | 99.9 cm² ½ × 14 × 15 × sin 108 M1 99.9 A1 | 2 |
A boat sails 18 km from A to B on a bearing of 050°. It then sails 8 km from B to C on a bearing of 125°.
Show that angle ABC = 105°.
Calculate the distance AC.
Calculate the bearing on which the boat must sail to return directly from C to A.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 105° uses co-interior / bearing of A from B = 230 M1 230 − 125 = 105 A1 | 2 |
| (b) | 21.5 km cosine rule M1 AC² = 18² + 8² − 2 × 18 × 8 × cos 105° M1 21.5 km A1 | 3 |
| (c) | 251° sine rule for angle BAC M1 angle BAC = 21.1° A1 251° A1 | 3 |
In triangle ABC, AB = 13 cm, AC = 8 cm and angle BAC = 62°.
Calculate BC.
Calculate angle ABC.
Calculate the shortest distance from C to the line AB.
Calculate the area of triangle ABC.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 11.6 cm BC2 = 82 + 132 − 2 × 8 × 13 × cos 62 M2 11.6 A1 | 3 |
| (b) | 37.4° sin B8 = sin 6211.63 M2 37.4 A1 | 3 |
| (c) | 7.06 cm 8 sin 62 M1 7.06 A1 | 2 |
| (d) | 45.9 cm² ½ × 8 × 13 × sin 62 M1 45.9 A1 | 2 |
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Meet Riyaz →Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in