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 sides (Sin = oh \frac{o}{h} ), Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} ), Use tangent ratio to calculate angles and sides (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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13.
Trigonometry
13.1
Angle in standard position
13.2
Coterminal angles
13.3
Reference angle
13.4
Find the exact value of trigonometric ratios
13.5
ASTC rule in trigonometry (All Students Take Calculus)
13.6
Unit circle
13.7
Converting between degrees and radians
13.8
Trigonometric ratios of angles in radians
13.9
Radian measure and arc length
13.10
Law of sines
13.11
Law of cosines
13.12
Applications of the sine law and cosine law
Sixth Year Maths