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.
1Explain2 marks
2022
Explain why the angle of elevation from A to B equals the angle of depression from B to A.
Markscheme and model answer locked
Unlock Question2Find3 marks
2022
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.
Markscheme and model answer locked
Unlock Question3Find3 marks
2022
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.
Markscheme and model answer locked
Unlock Question4find3 marks
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.).
Markscheme and model answer locked
Unlock Question5Write down1 mark
2026
Write down the angle of elevation from the boat to the top of the cliff.
Markscheme and model answer locked
Unlock Question6Find1 mark
2026
Find the angle of elevation of the top of the tower from that point.
Markscheme and model answer locked
Unlock Question7State1 mark
2023
The angle of elevation from point A to the top of a tower is always measured from which direction?
Markscheme and model answer locked
Unlock Question8Find1 mark
2022
A box has a square base of side 5 cm. A diagonal of the base has length:
Markscheme and model answer locked
Unlock Question9State1 mark
2023
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?
Markscheme and model answer locked
Unlock Question10State1 mark
2023
The angle of elevation and the angle of depression between two points are always:
Markscheme and model answer locked
Unlock Question11Calculate1 mark
2023
From a point 30 m from a building, the angle of elevation to the top is 54°. What is the height of the building?
Markscheme and model answer locked
Unlock Question12Interpret3 marks
2026
Interpret which boat is further from the cliff, and why.
Markscheme and model answer locked
Unlock Question13State1 mark
2022
In a 3D problem, you are finding the angle a line makes with a horizontal plane. Which step comes FIRST?
Markscheme and model answer locked
Unlock Question14Find1 mark
2022
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?
Markscheme and model answer locked
Unlock Question15State1 mark
2023
When solving a 3D trig problem involving a pyramid, which 2D triangle contains the angle between a slant edge and the base?
Markscheme and model answer locked
Unlock Question16Find1 mark
2023
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?
Markscheme and model answer locked
Unlock Question17Find1 mark
2022
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)?
Markscheme and model answer locked
Unlock Question18Find4 marks
2023
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.
Markscheme and model answer locked
Unlock Question19Find5 marks
2023
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.
Markscheme and model answer locked
Unlock Question20Find5 marks
2023
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.
Markscheme and model answer locked
Unlock QuestionReady to practice Topic 3.3?
Get instant AI feedback on your answers, view detailed markschemes, and track your progress across all IB Math AI SL topics.