Law of cosines

Law of cosines

There are times when the Law of Sines cannot solve the triangle because we encounter a triangle with either one of the following two scenarios – SAS (Side-angle-side), or SSS (Side-Side-Side). What should we do then? We consider using the Law of Cosines, which is another formula that models the relationship between the sides and the angles of any triangle. In this section, we will learn about the concept and the usage of the Law of Cosines, also known as the Cosines Rule.
Basic concepts: Use sine ratio to calculate angles and side (Sin = oh \frac{o}{h} ), Use cosine ratio to calculate angles and side (Cos = ah \frac{a}{h} ), Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a} ),
Related concepts: Quotient identities and reciprocal identities, Pythagorean identities, Sum and difference identities,

Lessons

For any △ABC\triangle \;ABC,
c2=a2+b2−2abcos(C)c^2=a^2+b^2-2ab\cos(C)
Use the Law of Cosine when given SSS (all sides), or SAS (angle-sandwich!)
  • Introduction
    • What is the law of cosines?
    • When and how do we use it?
  • 1.
    Find the length of side AB
    Law of cosines and side lengths of triangles
  • 2.
    Find angle E
    Law of cosines and angles in triangles
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30.
Sine Rule and Cosine Rule
30.1
Sine rule
30.2
Cosine rule
30.3
Sine rule and cosine rule word problems
GCE N(A)-Level Maths