Law of Cosines
The "Law of Cosines" can be used to calculate one side of a triangle when the angle opposite and the other two sides are known.
The "Law of Cosines" can be expressed as
$$ c^2 = a^2 + b^2 - 2 a b cos C \tag{1} $$
where
a, b and c = length of triangle sides (m, ft ..)
C = angle opposite side c (degrees)
Example - Calculate Side in Triangle
If side a = 1 m, side b = 1.3 m and angle C = 60 degrees - the side c can be calculated by modifying eq. 1 to
$$ c = \sqrt{ (1 m)^2 + (1.3 m)^2 - 2 (1 m) (1.3 m) cos (60 degrees) } = \underline{1.18} m $$
Law of Cosines Calculator
The generic calculator below can used to calculate the side c:
Law of Cosines - Excel Template
Related Topics
• Mathematics
Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.
Related Documents
AC - Active, Reactive and Apparent Power
Real, imaginary and apparent power in AC circuits.
Exponents - Powers and Roots
The laws of fractional and integer exponents.
Factorials
The product of all positive integers.
Fractions
Law of fractions
Hyperbolic Functions
Exponential functions related to the hyperbola.
Law of Sines
Calculate the angles in a generic triangle.
Law of Tangents
Triangles and law of tangents.
Pythagorean Theorem
Verifying square corners.
Right Angled Triangle
Right angled triangle equations.
Standard Differentials and Integrals
Equations for differentials and integrals.
Three-Phase Electrtical Motors - Power Factor vs. Inductive Load
Inductive loads and power factors with electrical three-phase motors.
Three-Phase Power - Equations
Electrical 3-phase equations.
Triangle
Triangle analytical geometry.
Trigonometric Functions
Sine, cosine and tangent - the natural trigonometric functions.
Vector Addition
Online vector calculator - add vectors with different magnitude and direction - like forces, velocities and more.
Wire Rope Slings
Sling angles and influence on capacity.