Unit 3: Geometry and Trigonometry
Topic 3.2: Triangle Trigonometry Questions
Practice 20 exam-style questions for IB Math AA SL Topic 3.2. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1Find2 marks
2026• Aimnova practice — 3.2.1
A right-angled triangle has hypotenuse 20 and an angle of 35°. Find the length of the side opposite the 35° angle, to 3 s.f.
Markscheme and model answer locked
Unlock Question2Find2 marks
2026• Aimnova practice — 3.2.1
A right-angled triangle has the side adjacent to angle θ equal to 9 and the opposite side equal to 5. Find θ to 3 s.f.
Markscheme and model answer locked
Unlock Question3Find2 marks
2026• Aimnova practice — 3.2.1
A right-angled triangle has legs of 8 and 15. Find the hypotenuse.
Markscheme and model answer locked
Unlock Question4Find2 marks
2026• Aimnova practice — 3.2.3
A triangle has sides 9 and 10 with an included angle of 40°. Find its area, to 3 s.f.
Markscheme and model answer locked
Unlock Question5Find2 marks
2026• Aimnova practice — 3.2.3
A triangle has sides 12 cm and 15 cm enclosing an angle of 25°. Find its area, to 3 s.f.
Markscheme and model answer locked
Unlock Question6Find3 marks
2026• Aimnova practice — 3.2.3
A triangle has area 84 cm², with two sides 13 cm and 14 cm. Find the included angle (give the acute value), to 3 s.f.
Markscheme and model answer locked
Unlock Question7Find3 marks
2026• Aimnova practice — 3.2.2
In triangle ABC, A = 35°, B = 80° and side a = 12. Find side b, to 3 s.f.
Markscheme and model answer locked
Unlock Question8Find3 marks
2026• Aimnova practice — 3.2.3
A triangle with sides 10 and 12 has area 30. Find the acute included angle.
Markscheme and model answer locked
Unlock Question9Find3 marks
2026• Aimnova practice — 3.2.1
In a right-angled triangle the hypotenuse is 25 and one leg is 7. (a) Find the other leg. (b) Find the angle opposite the leg of length 7.
Markscheme and model answer locked
Unlock Question10Find3 marks
2026• Aimnova practice — 3.2.2
In triangle ABC, a = 9, A = 55° and b = 7. Find angle B, to 3 s.f.
Markscheme and model answer locked
Unlock Question11Find2 marks
2026• Aimnova practice — 3.2.3
A field is a triangle with sides 30 m and 40 m and an included angle of 110°. Find its area, to 3 s.f.
Markscheme and model answer locked
Unlock Question12Find2 marks
2026• Aimnova practice — 3.2.1
A ladder of length 6 m leans against a wall, reaching 5 m up the wall. Find the angle the ladder makes with the ground, to 3 s.f.
Markscheme and model answer locked
Unlock Question13Find3 marks
2026• Aimnova practice — 3.2.1
A right-angled triangle has an angle of 40° and the side adjacent to it equal to 12. Find the hypotenuse to 3 s.f.
Markscheme and model answer locked
Unlock Question14Find3 marks
2026• Aimnova practice — 3.2.2
A triangle has b = 6, c = 10 and the included angle A = 45°. Find the third side a, to 3 s.f.
Markscheme and model answer locked
Unlock Question15Find3 marks
2026• Aimnova practice — 3.2.1
From a point on level ground, the angle of elevation to the top of a 30 m tower is 25°. Find the distance from the point to the base of the tower, to 3 s.f.
Markscheme and model answer locked
Unlock Question16Find3 marks
2026• Aimnova practice — 3.2.2
From a point P, town A is 8 km away and town B is 11 km away; the angle APB = 70°. Find the distance AB, to 3 s.f.
Markscheme and model answer locked
Unlock Question17Find4 marks
2026• Aimnova practice — 3.2.3
In triangle ABC, b = 8, c = 11 and the included angle A = 52°. (a) Find the area of the triangle. (b) Find side a, to 3 s.f.
Markscheme and model answer locked
Unlock Question18Find4 marks
2026• Aimnova practice — 3.2.2
A triangle has sides 5, 7 and 8. Find the largest angle, to 3 s.f.
Markscheme and model answer locked
Unlock Question19Find3 marks
2026• Aimnova practice — 3.2.3
Two sides of a triangle are 9 cm and 16 cm; its area is 54 cm². Find the two possible values of the included angle, to 3 s.f.
Markscheme and model answer locked
Unlock Question20Determine3 marks
2026• Aimnova practice — 3.2.2
A triangle has sides 4, 6 and 9. Determine whether it contains an obtuse angle, justifying your answer.
Markscheme and model answer locked
Unlock QuestionReady to practice Topic 3.2?
Get instant AI feedback on your answers, view detailed markschemes, and track your progress across all IB Math AA SL topics.