Practice SL 3.3—Angles of elevation and depression with authentic IB Mathematics Applications & Interpretation (AI) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.
Paper
Level
Question 1
SLPaper 2
A person standing on a cliff observes two boats at sea. Boat A is 100 meters away from the base of the cliff, observed at an angle of depression of 35°. The boat B is 200 meters away from the base of the cliff.
1.[3]
Assuming the cliff is perfectly perpendicular to the ground, calculate the height of the cliff using the given angle of depression to Boat A.
2.[3]
Find the angle of depression for boat B.
Question 2
SLPaper 1
Two planes, P and Q, depart from the same airport on different bearings. Plane P flies on a bearing of for 150 km, and plane Q flies on a bearing of for 200 km.
1.[3]
Calculate the distance between the two planes after completing their flights.
2.[3]
Another plane F is travelling with a bearing of Determine the smallest angle it makes with
Question 3
SLPaper 2
Two ships, A and B, leave a port, traveling in different directions. Ship A travels 60 km on a bearing of 030°, while ship B travels 80 km on a bearing of 120°.
1.[3]
Calculate the distance between the two ships after they complete their journeys.
Question 4
SL & HLPaper 1
A ship travels 30 km due East, then turns and sails 40 km due North.
1.[2]
Find the distance of the ship from its starting point, using trigonometric relationships.
2.[2]
Calculate the direction of the ship from its starting point as a bearing.
Question 5
SLPaper 1
The diagram below shows a helicopter hovering at point H, 380 m vertically above a lake. Point A is the point on the surface of the lake, directly below the helicopter. 
Minta is swimming at a constant speed in the direction of point Minta observes the helicopter from point C as she looks upward at an angle of 25°. After 15 minutes, Minta is at point B and she observes the same helicopter at an angle of 40°.
1.[1]
Write down the size of the angle of depression from H to C.
2.[2]
Find the distance from A to C.
3.[3]
Find the distance from B to C.
4.[1]
Find Minta's speed, in metres per hour.