余弦定理，一般是指在欧氏平面的 三角形 中关于三边长度和一个角度 余弦 值的恒等式。 借助余弦定理，可以在已知三角形两边及其 夹角 的情况下，算出第三边的长度；也可以在已知三边长度的情况下，算出各角的余弦值。 余弦定理可以用于解三角形、构造恒等式等。 余弦定理可以推广至四边形、四面体、高维空间、非欧空间等，具有深刻的内涵。 其中，，为的三边长。 余弦定理是一条重要的几何定理，其发展贯穿了古代数学的演进，涉及多个文明的贡献。 最早关于余弦 …

The Law of Sines (or Sine Rule) is very useful for solving triangles: a sin A = b sin B = c sin C. It works for any triangle:

In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

Law of sines defines the ratio of sides of a triangle and their respective sine angles are equivalent to each other. The other names of the law of sines are sine law, sine rule and sine formula. The law of sine is used to find the unknown angle or the side of an oblique triangle.

We can use the sine rule to work out a missing angle or side in a triangle when we have information about an angle and the side opposite it, and another angle and the side opposite it. This is the sine rule:

Revise how to use the sine and cosine rules to find missing angles and sides of triangles as part of National 5 Maths.

The Law of Sines (sine rule) is an important rule relating the sides and angles of any triangle (it doesn't have to be right-angled!): If a, b and c are the lengths of the sides opposite the angles A, B and C in a triangle, then: a = b = c. sinA sinB sinC. If you wanted to find an angle, you can write this as: sinA = sinB = sinC. a b c.

The sine rule formula gives the ratio of the sides and angles of a triangle. The sine rule can be explained using the expression, a/sinA = b/sinB = c/sinC. Here a, b, c are the length of the sides of the triangle, and A, B, C are the angles of the triangle.

Given the following triangle ABC ABC with corresponding side lengths a, b a,b and c c: the sine rule or law of sines is the following identity: \frac { a} { \sin (A)} = \frac {b} {\sin (B)} = \frac {c} {\sin (C)}. sin(A)a = sin(B)b = sin(C)c. We will prove the first identity. \frac { a} { \sin (A)} = \frac {b} {\sin (B)}. sin(A)a = sin(B)b.

Tutorial on the law of sines and cosines and on how to decide which formula to use in triangle problems.