TopicGeneral Maths
Trigonometry · SS1–SS2
Elevation, depression & bearings
Using trigonometry for heights and distances: angles of elevation and depression, and bearings.
- Before this
- Trigonometric ratios
Learn
- 1Angles of elevation and depressionMeasure from the horizontal, spot that elevation and depression are equal, and handle eye height, two angles, ladders and shadows.Done20 min
- 2BearingsMeasure clockwise from north at the right point, write three figures, find back bearings, read compass directions like N 40° E, and split a journey into north and east parts.Done18 min
- 3Drawing the bearing diagramThe step that decides most bearing questions: turn the words into a diagram, one sentence at a time, then find the angle inside the triangle.Done15 min
Practise
Answer elevation, depression & bearings questions one at a time. You'll know straight away whether you're right, with hints and the working step by step.
Your progress is saved on this device as you practise. No account needed.
Past questions (94)
From 1983–2025: 64 WAEC, 5 NECO, 25 JAMB. Theory questions first, then objective, newest first.
Theory (54)
- WAEC 2025 · Paper 2 · Q10A man travels from on a bearing of to , away. From he travels to on a bearing of . If …
- WAEC 2025 · Paper 2 · Q4A pack of 52 playing cards is shuffled and one card is drawn. Find the probability that it is either a five or a red nine.
- WAEC 2024 · Paper 2 · Q8Two observers, Abu and Badu, apart, observe a bird on top of a vertical pole from the same side of the pole. The angles of elevation …
- WAEC 2023 · Paper 2 · Q10In a town, Chief resides away on a bearing of from the palace , while Chief resides on a bearing of …
- WAEC 2023 · Paper 2 · Q5A boy stands at a point on the same horizontal level as the foot, , of a vertical building. He observes an object on the top, , of …
- WAEC 2023 · Paper 2 · Q10In a large library, Adamu is seated away from Uju on a bearing of . Bola is away from Adamu on a bearing …
- WAEC 2023 · Paper 2 · Q8A tree is due south of a building. Musa is standing due west of the tree. (i) Illustrate the information on a diagram. …
- WAEC 2022 · Paper 2 · Q13The diameter of a cylinder closed at both ends is . If the total surface area is , calculate the height.
- WAEC 2022 · Paper 2 · Q5A bird perches on the top of a slanted tree of length . If the bird is vertically above the ground, (i) illustrate …
- WAEC 2022 · Paper 2 · Q10Two canoes and started from a shore at the same time. sails at on a bearing of while sails at …
- WAEC 2022 · Paper 2 · Q3A tower and a building are on the same horizontal ground. An engineer on the top of the tower, high, observes that the angle of …
- WAEC 2021 · Paper 2 · Q10A cottage is on a bearing of and from Dogbe's and Mamu's farms respectively. If Dogbe walked and Mamu …
- WAEC 2021 · Paper 2 · Q3The points , and are located such that is south of , and is from on a bearing of . …
- WAEC 2021 · Paper 2 · Q12The angle of depression of a boat from the midpoint of a vertical cliff is . If the boat is away from the foot of the …
- WAEC 2021 · Paper 2 · Q4 and are tangents to the circle with centre at and , and is a point on the major arc . If , …
- WAEC 2021 · Paper 2 · Q8A boat sails from to on a bearing of , then to on a bearing of . is on a bearing of …
- WAEC 2020 · Paper 2 · Q9Two cyclists and leave town at the same time. Cyclist travels at the rate of on a bearing of and …
- WAEC 2020 · Paper 2 · Q5A ladder long leans against a vertical wall at an angle of to the ground. If the ladder slips down the wall , …
- WAEC 2020 · Paper 2 · Q8In a class, students were taught French, Mathematics and Economics. The teachers observed that 5 liked all the 3 subjects, 9 French and Mathematics, …
- WAEC 2020 · Paper 2 · Q3An aeroplane flies from town on a bearing of to town . It then flies to town on a bearing …
- WAEC 2020 · Paper 2 · Q9An aeroplane flies from point to point on a bearing of . It then flies from point to point , …
- WAEC 2019 · Paper 2 · Q8Solve the inequality .
- WAEC 2019 · Paper 2 · Q11A ladder long leans against a vertical wall at an angle of to the ground. The ladder is then pushed up …
- WAEC 2019 · Paper 2 · Q7In the diagram, is a chord of a circle with centre . If and the perimeter of triangle is , …
- WAEC 2019 · Paper 2 · Q12A town is from a lorry station, , on a bearing . Another town, , is from on a bearing . …
- WAEC 2018 · Paper 2 · Q7Find the equation of the line passing through the points and .
- WAEC 2018 · Paper 2 · Q1Evaluate without using a calculator: .
- WAEC 2018 · Paper 2 · Q12A man starts from a point and walks to on a bearing of . He then walks due south to a point which is …
- WAEC 2018 · Paper 2 · Q6A textbook company discovered that the profit made from selling its books is given by , where is the number of textbooks …
- WAEC 2017 · Paper 2 · Q10Given that , , find .
- WAEC 2017 · Paper 2 · Q3The angle of depression of a point on the ground from the top of a building is . If the distance from to the foot of …
- WAEC 2017 · Paper 2 · Q10Three dormitories , and are such that and are and from respectively. The bearings …
- WAEC 2017 · Paper 2 · Q9An aeroplane flies 100 km from town on a bearing of to town . It then flies 300 km due west to town . (i) Illustrate this …
- WAEC 2016 · Paper 2 · Q5In the diagram, is a parallelogram, is a straight line, , () and the area …
- WAEC 2016 · Paper 2 · Q4Solve the inequality .
- WAEC 2016 · Paper 2 · Q8An eagle flies from point to , a distance of , on a bearing of N W. It then changes direction and flies …
- WAEC 2015 · Paper 2 · Q10Without using mathematical tables or calculators, simplify .
- WAEC 2014 · Paper 2 · Q12Given that , , calculate, correct to the nearest degree, the value of .
- WAEC 2014 · Paper 2 · Q10(i) Solve the inequality . (ii) Illustrate the solution on a number line.
- WAEC 2013 · Paper 2 · Q13When one end of a ladder is placed against a vertical wall at a point 5 metres above the ground, the ladder makes an angle of …
- WAEC 2013 · Paper 2 · Q5A boy tall stands away from the foot of a vertical lamp pole high. If the lamp is at the tip of the …
- WAEC 2013 · Paper 2 · Q10Town is due north of . The bearing of town from is . If is from , calculate:
- WAEC 2013 · Paper 2 · Q2The diagram shows a triangular prism with and . If and …
- WAEC 2012 · Paper 2 · Q8A point is away from the foot of a tower on the same horizontal ground. From the point , the angles of elevation of …
- WAEC 2012 · Paper 2 · Q10If , find .
- WAEC 2011 · Paper 2 · Q10The total surface areas of two spheres are in the ratio . If the radius of the smaller sphere is , find, correct to the …
- WAEC 2010 · Paper 2 · Q2The angle of depression of a boat from the mid-point of a vertical cliff is . If the boat is from the foot of the cliff, …
- WAEC 2010 · Paper 2 · Q9In the diagram, , , the bearing of from is and the bearing of from is . …
- WAEC 2010 · Paper 2 · Q11A ship is due east of a harbour. Another ship is also from the harbour but on a bearing of from …
- WAEC 2010 · Paper 2 · Q3In a right-angled triangle, . Evaluate .
- WAEC 2009 · Paper 2 · Q7A woman looking out from the window of a building at a height of 30 m observed that the angle of depression of the top of a flag pole was . …
- WAEC 2009 · Paper 2 · Q13The pilot of an aircraft 2000 metres above sea level observes at an instant that the angles of depression of two boats, which are in a direct …
- WAEC 2008 · Paper 2 · Q1If , evaluate .
- WAEC 2008 · Paper 2 · Q9The triangle has sides , and . Calculate the: (i) largest angle of the triangle; …
Objective (40)
- WAEC 2025 · Paper 1 · Q45The bearings of and from are and . If and , find .
- NECO 2024 · Paper 1 · Q37A boy walks due west. He then changes direction and walks on a bearing of until he is south-west of his starting point. …
- NECO 2024 · Paper 1 · Q39A bird on top of a building high observes a prey away from the foot of the building. Calculate the angle of depression …
- WAEC 2024 · Paper 1 · Q24Given that is on a bearing of from , how far south of is ?
- WAEC 2024 · Paper 1 · Q44A cliff on the bank of a river is high. A boat on the river is away from the cliff. Calculate, correct to the nearest …
- NECO 2023 · Paper 1 · Q44An aeroplane flies from a town on a bearing of to a town , a distance of . It then changes course and flies …
- NECO 2023 · Paper 1 · Q45If the angle of depression of a boy standing on the ground from the top of a house is , what is the angle of elevation of the top of …
- WAEC 2023 · Paper 1 · Q24Mrs Kebeh stands at a distance of away from a building of vertical height . If Kebeh is tall, find the …
- WAEC 2023 · Paper 1 · Q35The angle of elevation of the top of a building from a point on the ground is . If the height of the building is , …
- WAEC 2023 · Paper 1 · Q38John was facing S35°E. If he turned in the anticlockwise direction, find his new direction.
- NECO 2022 · Paper 1 · Q42The angle of elevation of the top of a wall from a point on the ground is . If m, how far is from the foot of …
- WAEC 2022 · Paper 1 · Q28A boy tall stood away from a tree of height . Calculate, correct to the nearest degree, the angle of …
- WAEC 2021 · Paper 1 · Q28From a point , a man moves due west and then due south to another point . Calculate the bearing of from …
- WAEC 2020 · Paper 1 · Q25A fence tall is away from a tree of height . Calculate the angle of elevation of the top of the tree …
- WAEC 2019 · Paper 1 · Q37From the top of a vertical cliff high, a boat at sea can be sighted away on the same horizontal level as the foot …
- JAMB 2017 · UTME · Q13The shadow of a pole high is long. Find the angle of elevation of the sun.
- JAMB 2015 · UTME · Q32The angle of elevation of a building from a measuring instrument placed on the ground is . If the building is high, how …
- JAMB 2012 · UTME · Q36A man stands on a tree high and sees a boat at an angle of depression of . Find the distance of the boat from the base …
- JAMB 2011 · UTME · Q35A man walks due West from a point to . He then walks due North to a point . Find the bearing of from …
- JAMB 2004 · UME · Q34The shadow of a pole m high is 5 m. Find the angle of elevation of the sun.
- JAMB 2003 · UME · Q29An aeroplane flies due north from airport to and then due east to . If is equidistant from and , find the bearing of …
- JAMB 2002 · UME · Q21A hunter 1.6 m tall views a bird on top of a tree at an angle of . If the distance between the hunter and the tree is 10.4 m, find …
- JAMB 2001 · UME · Q31The bearings of and from a common point are and respectively. If and are also equidistant from , …
- JAMB 2000 · UME · Q26A ship sails a distance of 50 km in the direction SE and then 50 km in the direction NE. Find the bearing of the ship from …
- JAMB 1999 · UME · Q27A man 1.7 m tall observes a bird on top of a tree at an angle of elevation of . If the distance between the man's head and the bird …
- JAMB 1999 · UME · Q30From a point , the bearings of two points and are NW and NE respectively. If the bearing of from is NE …
- JAMB 1998 · UME · Q37From the top of a vertical mast 150 m high, two huts on the same ground level are observed, one due east and the other due west of the mast. …
- JAMB 1995 · UME · Q35A schoolboy lying on the ground 30 m away from the foot of a water tower observes that the angle of elevation of the top of the tower is . …
- JAMB 1994 · UME · Q37The angle of depression of a boat from the top of a cliff 10 m high is . How far is the boat from the foot of the cliff?
- JAMB 1993 · UME · Q40In the figure, , and are on level ground with m, and is vertical. The angles of elevation of from and are …
- JAMB 1991 · UME · Q39A flagstaff stands on top of a vertical tower. A man standing 60 m from the tower observes that the angles of elevation of the top and bottom …
- JAMB 1991 · UME · Q42From a point , 60 m north of , a man walks m eastwards to another point . Find the bearing of from .
- JAMB 1989 · UME · Q41The pilot of an aeroplane flying 10 km above the ground towards a landmark sees the landmark at angles of depression of and then . …
- JAMB 1988 · UME · Q39From a point m away from a tree, a man finds that the angle of elevation of the top of the tree is . If he measures this …
- JAMB 1988 · UME · Q40Alero starts a 3 km walk from on a bearing of . She then walks 4 km on a bearing of to . What is the bearing of …
- JAMB 1987 · UME · Q40From two points and , 8 m apart and in line with a pole, the angles of elevation of the top of the pole are and …
- JAMB 1986 · UME · Q34The angle of elevation of the top of a vertical tower 50 m high from a point on the ground is . From a point on the opposite …
- JAMB 1986 · UME · Q35A girl walks 45 m in the direction from a point to a point . She then walks 24 m in the direction from to …
- JAMB 1985 · UME · Q32The bearing of a bird on a tree from a hunter on the ground is NE. What is the bearing of the hunter from the bird?
- JAMB 1983 · UME · Q37A ship leaves a port and sails 30 km due south. Then it sails 60 km due west. What is the bearing of from ?