Unit 3: Geometry and Trigonometry
Topic 3.3: Applications of Trigonometry Questions
Practice 20 exam-style questions for IB Math AI SL Topic 3.3. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1State1 mark
2023• AI SL P1
A and B stand on level ground. A is 80 m from the base of a tree. The angle of elevation from A to the top of the tree is 22°. Which expression gives the tree's height?
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2022• AI SL P1
A box has a square base of side 5 cm. A diagonal of the base has length:
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2023• AI SL P1
The angle of elevation and the angle of depression between two points are always:
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2023• AI SL P1
From a point 30 m from a building, the angle of elevation to the top is 54°. What is the height of the building?
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A surveyor stands 65 m from the base of a flagpole and measures the angle of elevation to the top to be 28°. Find the height of the flagpole (to 1 d.p.).
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2022• AI SL P1
Explain why the angle of elevation from A to B equals the angle of depression from B to A.
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2022• AI SL P1
A boat is 240 m from the base of a cliff. The angle of elevation from the boat to the top of the cliff is 14°. A seagull sits on top of the cliff. Find the straight-line distance from the boat to the seagull.
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2023• AI SL P1
The angle of elevation from point A to the top of a tower is always measured from which direction?
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2022• AI SL P1
A communications antenna is mounted on the roof of a building. The building is 40 m tall and the antenna is 12 m above the roof. From a point P on the ground 60 m from the base, find the angle of elevation to the top of the antenna.
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2022• AI SL P1
A lighthouse keeper at height h = 35 m looks down at a ship. The angle of depression is 15°.
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2022• AI SL P2
Point A is at the base of a vertical cliff. Point B is 50 m from A along flat ground. A rock R is embedded in the cliff face: it is 30 m above A and 10 m horizontally from A (in the direction away from B).
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2023• AI SL P1
An observer looks down at a boat. The angle of depression is 28°. If the observer is 50 m above the water, what is the horizontal distance to the boat?
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2022• AI SL P1
A cuboid has length 4 m, width 3 m and height 2 m. What is the length of the space diagonal (corner to opposite corner)?
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2022• AI SL P1
In a 3D problem, you are finding the angle a line makes with a horizontal plane. Which step comes FIRST?
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2022• AI SL P1
A tent has a rectangular base 4 m × 3 m. The vertical pole in the centre is 2 m high. What is the angle the pole makes with a line from the top of the pole to a corner of the base?
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2023• AI SL P1
When solving a 3D trig problem involving a pyramid, which 2D triangle contains the angle between a slant edge and the base?
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2023• AI SL P2
A right pyramid has a rectangular base 8 m × 6 m and vertical height 5 m. Find the angle between the face containing the 8 m edge and the base.
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2023• AI SL P1 TZ1
A hot-air balloon is at H, directly above point B on the ground. A woman at A on the ground, with AB horizontal, observes the balloon. The angle of elevation from A to H is 40°. Building height BH = 156 m.
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2023• AI SL P2
An engineer is planning a ski run. Point A is at the top of the slope at altitude 1800 m; point B is at the base at altitude 1200 m. The horizontal distance from A to B is 750 m.
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2022• AI SL P2
A ship P is 20 km due north of port O. Ship Q is 15 km due east of O. Both ships are at sea level. A helicopter at H is 3 km directly above O.
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