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Law of Tangents

The law of tangents is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides.

The difference between the lengths of the first and second sides divided by the sum of the lengths of the first and second sides equals the cotangent of the average of the angles opposite the first and second sides times the tangent of half the difference between the angle opposite the first side and the angle opposite the second side.

Formula

(QuantityVariable["a", "Length"] - QuantityVariable["b", "Length"])/(QuantityVariable["a", "Length"] + QuantityVariable["b", "Length"]) == Cot[(QuantityVariable["α", "Angle"] + QuantityVariable["β", "Angle"])/2]*Tan[(QuantityVariable["α", "Angle"] - QuantityVariable["β", "Angle"])/2]

symbol description physical quantity
a first side length "Length"
b second side length "Length"
α angle opposite first side "Angle"
β angle opposite second side "Angle"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Law of Tangents"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Law of Tangents"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Law of Tangents"], {QuantityVariable["\[Beta]","Angle"] -> Quantity[60, "AngularDegrees"]}]
Out[3]=

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