Sine rule, cosine rule, tangent rule and 3D
Solve triangles drawn to scale with the sine rule, the cosine rule and the tangent rule, then use right-angled triangles to find an angle in a cuboid.
- UK: Year 11
- France: grade 11
- Germany: grade 10
- Iran: grade 11
- Afghanistan: grade 11
- Syria: grade 11
- Ukraine: grade 9
- Russia: grade 9
Guide
For Afghan Grade 11 (chapter 2: sine rule, cosine rule, tangent rule), Iran Grade 11 and GCSE. The figures are drawn to scale (1 unit is 1 cm); the known sides and angles are shown and the unknown one is hidden. Table values are printed in the mission.
In triangle ABC the side a is opposite the angle A. The sine rule is asin A = bsin B = csin C: use it when you know an angle and the side opposite it.
The cosine rule is a2 = b2 + c2 − 2bccosA: use it for two sides and the angle between them, or for three sides. The tangent rule is a − ba + b = tanA − B2tanA + B2: use it for two sides and the angle between them, to find the other two angles.
In 3D, find a right-angled triangle that contains the angle. The angle between a line and a plane is the angle between the line and its shadow on the plane.