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.
A person standing on a cliff observes two boats at sea. Boat A is metres away from the base of the cliff, observed at an angle of depression of . Boat B is metres away from the base of the cliff.
Assuming the cliff is perfectly perpendicular to the ground, calculate the height of the cliff using the given angle of depression to Boat A.
Find the angle of depression for Boat B.
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.
Calculate the distance between the two planes after completing their flights.
Another plane F is travelling on a bearing of . Determine the smallest angle between the path of plane F and the path of plane Q.
Two ships, A and B, leave a port, travelling in different directions. Ship A travels km on a bearing of , while ship B travels km on a bearing of .
Calculate the distance between the two ships after they complete their journeys.
A ship travels 30 km due East, then turns and sails 40 km due North.
Calculate the distance of the ship from its starting point.
Calculate the direction of the ship from its starting point as a bearing.
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 A. 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°.
Write down the size of the angle of depression from H to C.
Find the distance from A to C.
Find the distance from B to C.
Find Minta's speed, in metres per hour.
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.
A person standing on a cliff observes two boats at sea. Boat A is metres away from the base of the cliff, observed at an angle of depression of . Boat B is metres away from the base of the cliff.
Assuming the cliff is perfectly perpendicular to the ground, calculate the height of the cliff using the given angle of depression to Boat A.
Find the angle of depression for Boat B.
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.
Calculate the distance between the two planes after completing their flights.
Another plane F is travelling on a bearing of . Determine the smallest angle between the path of plane F and the path of plane Q.
Two ships, A and B, leave a port, travelling in different directions. Ship A travels km on a bearing of , while ship B travels km on a bearing of .
Calculate the distance between the two ships after they complete their journeys.
A ship travels 30 km due East, then turns and sails 40 km due North.
Calculate the distance of the ship from its starting point.
Calculate the direction of the ship from its starting point as a bearing.
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 A. 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°.
Write down the size of the angle of depression from H to C.
Find the distance from A to C.
Find the distance from B to C.
Find Minta's speed, in metres per hour.