TopicGeneral Maths
Trigonometry · SS2
Sine & cosine rules
The sine and cosine rules for triangles that are not right-angled.
- Before this
- Trigonometric ratios
Learn
- 1The sine rule and the cosine ruleTwo rules for triangles without a right angle: which one to use, how to set it out, and the sign of cos for obtuse angles.Done20 min
- 2Bearings with any triangleThe hardest bearing questions: find the angle inside the triangle from the bearings, then use the cosine rule for the distance and the sine rule for the new bearing.Done15 min
Practise
Answer sine & cosine rules 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 (40)
From 1983–2023: 18 WAEC, 1 NECO, 21 JAMB. Theory questions first, then objective, newest first.
Theory (18)
- 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 · Q10In a large library, Adamu is seated away from Uju on a bearing of . Bola is away from Adamu on a bearing …
- 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 · Q8In an isosceles triangle , and . Find, correct to two significant figures, the: …
- 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 · Q9In the diagram, is on and is on with . , , and …
- 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 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 2014 · Paper 2 · Q12Given that , , calculate, correct to the nearest degree, the value of .
- WAEC 2013 · Paper 2 · Q8If , , are consecutive terms of a geometric progression (G.P.) with constant ratio , find the: (i) value of ; …
- WAEC 2013 · Paper 2 · Q10Town is due north of . The bearing of town from is . If is from , calculate:
- 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 · 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 2009 · Paper 2 · Q9 (lat N, long E), (lat N, long W) and (lat S, long E) are three points …
- WAEC 2008 · Paper 2 · Q9The triangle has sides , and . Calculate the: (i) largest angle of the triangle; …
- WAEC 2008 · Paper 2 · Q12In the diagram, , , and . Calculate .
Objective (22)
- NECO 2022 · Paper 1 · Q36In an isosceles triangle , where cm and , calculate , correct …
- JAMB 2015 · UTME · Q19In , , and . If the bisector of meets at , what is …
- JAMB 2015 · UTME · Q39In , units, units and units. If the bisector of angle meets at , calculate .
- JAMB 2015 · UTME · Q4A force of 5 units acts on a particle in the direction due east and another force of 4 units acts on the particle in the direction north-east. …
- JAMB 2013 · UTME · Q33In triangle , , and . Find .
- JAMB 2004 · UME · Q33In the triangle shown, the base angles are and , the side opposite the angle is 15 cm and the side opposite the …
- JAMB 2001 · UME · Q26A point moves such that it is equidistant from the points and . Find when cm and .
- JAMB 2001 · UME · Q32Find the value of in the diagram (an isosceles triangle with sides , and base ).
- JAMB 1999 · UME · Q25In triangle , m, m and . Find the length .
- JAMB 1998 · UME · Q35In the diagram, is a straight line, , , and . Find the sine of .
- JAMB 1997 · UME · Q36In a triangle , if , cm and cm, calculate the length of the side .
- JAMB 1997 · UME · Q37In the figure, is a triangle with cm and cm; is produced to , making . If , …
- JAMB 1995 · UME · Q36 is a triangle with m, and . Calculate the length of .
- JAMB 1993 · UME · Q41If two angles of a triangle are each and the longest side is 10 cm, calculate the length of each of the other sides.
- JAMB 1990 · UME · Q40In the figure, , and cm. Calculate .
- JAMB 1989 · UME · Q37In , and cm. Find .
- JAMB 1988 · UME · Q42In triangle , cm, cm and . Find the longest side of the triangle.
- JAMB 1986 · UME · Q39In , , and . Determine the cosine of angle .
- JAMB 1985 · UME · Q26In , cm, cm, cm and . Find .
- JAMB 1984 · UME · Q28In triangle , , cm and cm. Find .
- JAMB 1984 · UME · Q29The sides of a triangle are cm, cm and cm. If the cosine of the largest angle is , find the value of .
- JAMB 1983 · UME · Q46In a triangle , cm, cm, cm and . Find the angles and .