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.

1Find3 marks
2022
A zip-wire runs from a platform at height 12 m to the ground. The wire makes an angle of 18° with the horizontal. Find the length of the wire.
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2find2 marks
In an equilateral triangle of side 12, find the altitude (perpendicular from a vertex to the opposite side).
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3find2 marks
A right triangle has legs 9 cm and 12 cm. Find the hypotenuse.
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4Find4 marks
2022
A right triangle has hypotenuse 20 cm and one angle of 55°. Find the lengths of both legs.
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5find3 marks
A spotlight at the top of a 20 m tower shines down at an angle of depression 35°. Find the distance from the base of the tower to where the light hits the ground.
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6find3 marks
From a coastal observation tower, the angle of depression to a ship is 28°. The tower is 45 m above sea level. Find the distance from the base of the tower to the ship.
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7find2 marks
In a right triangle, the longest side is 41 and the shortest is 9. Find the angle opposite the shortest side.
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8find2 marks
In a right triangle, θ = 5°, Adj = 100. Find Opp.
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9find2 marks
In a right triangle, the angle opposite the longer leg is 60°. The shorter leg has length 7. Find the hypotenuse.
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10Find3 marks
2022
A tree casts a shadow of length 15 m. The angle of elevation from the tip of the shadow to the top of the tree is 38°. Find the height of the tree.
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11State1 mark
2023
In triangle ABC, AB = 8 cm, angle A = 50° and angle B = 70°. Which formula correctly starts the calculation of BC?
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12find2 marks
An aeroplane is 4 km above the ground at horizontal distance 7 km from an airport. Find the straight-line distance from the plane to the airport.
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13find2 marks
A right triangle has hypotenuse 13 and adjacent 5. Find the angle θ at the vertex adjacent to Adj.
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14find3 marks
In a right triangle, θ = 15° and Adj = 30. Find Opp.
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15find3 marks
A vertical mast is 30 m tall. A guy wire from the top makes an angle of 50° with the ground. Find the length of the guy wire.
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16find3 marks
A car drives up a hill 100 m long at an incline of 15° from horizontal. Find the vertical height gained and the horizontal distance.
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17find4 marks
A 5 m ladder leans on a wall. The TOP of the ladder is 4 m above the ground. Find the angle the ladder makes with the ground and how far the foot is from the wall.
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18find3 marks
An aircraft is climbing at 20° above horizontal at 200 m/s. Find its rate of climb (vertical) and horizontal speed.
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19find3 marks
In a right triangle, θ = 50°, hypotenuse = 8 cm. Find the adjacent side.
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20find3 marks
From the top of a 200 m skyscraper, the angle of depression to a point on the ground is 70°. Find the horizontal distance to that point.
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