Unit 3: Geometry and Trigonometry

Topic 3.2: Trigonometry: Right and Non-Right Triangles Questions

Practice 20 exam-style questions for IB Math AI 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
In a right triangle, the legs are 11 and 60. Find the hypotenuse.
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2find3 marks
In triangle ABC, a = 8 cm, b = 11 cm and the included angle C = 47°. Find side c.
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3find3 marks
In a right triangle, the angle is 22°, hypotenuse is 50 m. Find the height (vertical side opposite to 22°).
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4find3 marks
From a window 12 m up, the angle of depression to an object on the ground is 35°. Find the horizontal distance from the building base to the object.
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5find2 marks
In a right triangle, the area is 24 cm² and one leg = 6. Find the other leg.
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6find1 mark
A right triangle has Opp = 1 and Hyp = 2. Find θ.
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7find1 mark
From point A, the bearing of point B is 040°. From point B, the bearing of A is 220°. Find the bearing FROM B as a single calculation: A is on bearing 220° from B (back bearing = forward + 180° mod 360°). Verify.
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8find2 marks
In a right triangle, Adj = 14, Opp = 7. Find θ.
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9find3 marks
A ramp has a 1 m vertical rise over 8 m horizontal length. Find the angle of inclination.
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10find2 marks
A boat sails 12 km north then 9 km east. Find the straight-line distance back to start.
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11find2 marks
A staircase is 2.4 m long and makes an angle of 30° with the floor. Find the vertical height it rises.
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12find3 marks
In triangle PQR, angle P = 38°, angle Q = 72°, and side p = 10 cm. Find side q (to 3 s.f.).
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13find3 marks
A ladder of length L makes an angle of 70° with the ground when leaning against a wall, with foot 1.5 m from the wall. Find L.
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14find1 mark
In a right triangle, tan θ = √3 exactly. Find θ.
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15find3 marks
A right triangle has Adj = 5 and θ = 25°. Find Hyp.
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16find2 marks
In a 45-45-90 triangle, the legs are each 6. Find the hypotenuse exactly.
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17find3 marks
A vertical post of unknown height casts a shadow 18 m long when the angle of elevation of the sun is 42°. Find the height.
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18find2 marks
In a right triangle, θ = 55° and adjacent = 12. Find the hypotenuse.
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19find2 marks
A right triangle has hypotenuse 25 cm and one leg 7 cm. Find the other leg.
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20find3 marks
A triangle has two sides 14 cm and 9 cm with included angle 35°. Find its area.
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