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.
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In a right triangle, the legs are 11 and 60. Find the hypotenuse.
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In triangle ABC, a = 8 cm, b = 11 cm and the included angle C = 47°. Find side c.
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In a right triangle, the angle is 22°, hypotenuse is 50 m. Find the height (vertical side opposite to 22°).
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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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In a right triangle, the area is 24 cm² and one leg = 6. Find the other leg.
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A right triangle has Opp = 1 and Hyp = 2. Find θ.
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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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In a right triangle, Adj = 14, Opp = 7. Find θ.
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A ramp has a 1 m vertical rise over 8 m horizontal length. Find the angle of inclination.
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A boat sails 12 km north then 9 km east. Find the straight-line distance back to start.
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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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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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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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In a right triangle, tan θ = √3 exactly. Find θ.
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A right triangle has Adj = 5 and θ = 25°. Find Hyp.
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In a 45-45-90 triangle, the legs are each 6. Find the hypotenuse exactly.
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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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In a right triangle, θ = 55° and adjacent = 12. Find the hypotenuse.
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A right triangle has hypotenuse 25 cm and one leg 7 cm. Find the other leg.
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A triangle has two sides 14 cm and 9 cm with included angle 35°. Find its area.
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