Free Right-angled triangles questions for IGCSE Mathematics (0580), part of Trigonometry. Each question has the answer and the marking points an examiner would look for.
Generate a full Right-angled Triangles worksheet →All Trigonometry questionsTwo points A and B are on horizontal ground, 80 m apart, in a straight line with the foot of a vertical tower. B is between A and the tower.
The angle of elevation of the top of the tower from A is 23° and from B is 35°.
Calculate the height of the tower.
| Part | Answer and marking points | Marks |
|---|---|---|
| 86.2 m h = (80 + x) tan 23 and h = x tan 35, where x = distance from B to tower M2 equate and solve for x M1 x = 123 A1 86.2 A1 | 5 |
The diagram shows triangle ABC.
Calculate the length of AC.
| Part | Answer and marking points | Marks |
|---|---|---|
| 9.16 cm ACsin 43 = 11sin 55 M2 M1 for a correct implicit sine rule 9.16 A1 | 3 |
Two points A and B are on horizontal ground, 40 m apart, in a straight line with the foot of a vertical tower. B is between A and the tower.
The angle of elevation of the top of the tower from A is 26° and from B is 44°.
Calculate the height of the tower.
| Part | Answer and marking points | Marks |
|---|---|---|
| 39.4 m h = (40 + x) tan 26 and h = x tan 44, where x = distance from B to tower M2 equate and solve for x M1 x = 40.8 A1 39.4 A1 | 5 |
Two points A and B are on horizontal ground, 30 m apart, in a straight line with the foot of a vertical tower. B is between A and the tower.
The angle of elevation of the top of the tower from A is 30° and from B is 41°.
Calculate the height of the tower.
| Part | Answer and marking points | Marks |
|---|---|---|
| 51.6 m h = (30 + x) tan 30 and h = x tan 41, where x = distance from B to tower M2 equate and solve for x M1 x = 59.3 A1 51.6 A1 | 5 |
Two points A and B are on horizontal ground, 50 m apart, in a straight line with the foot of a vertical tower. B is between A and the tower.
The angle of elevation of the top of the tower from A is 27° and from B is 35°.
Calculate the height of the tower.
| Part | Answer and marking points | Marks |
|---|---|---|
| 93.6 m h = (50 + x) tan 27 and h = x tan 35, where x = distance from B to tower M2 equate and solve for x M1 x = 134 A1 93.6 A1 | 5 |
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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