Law of Tangents

Triangles and law of tangents. Calculate the angles or sides of a triangle using the Law of Tangents, Pythagorean theorem, Law of sines, and related formulas.

Law of Tangents

The Law of Tangents can be expressed as:

(a + b) / (a - b) = tan(1/2 (A + B)) / tan(1/2 (A - B))

Where:

  • a, b, c = length of sides in triangle (m, ft, ...)
  • A, B, C = angles in the triangle (degrees)

Related Formulas

Pythagorean Theorem

a² + b² = c²

Law of Sines

a / sin(A) = b / sin(B) = c / sin(C)

Calculate Angles from Sides

  • A = arccos((b² + c² - a²) / (2bc))
  • B = arccos((a² + c² - b²) / (2ac))
  • C = arccos((a² + b² - c²) / (2ab))
Calculator

Inputs

Results

Angle A-- degrees
Angle B-- degrees
Angle C-- degrees
PropertyValueUnit
Side a5m
Side b6m
Side c7m
Angle A38.21°degrees
Angle B46.57°degrees
Angle C95.22°degrees