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Spherical Law of Sines

The spherical law of sines is an equation relating the angular lengths of the sides of a triangle (any shape) to the sines of its angles.

The cosecant of the angle opposite the first side times the sine of the angular length of the first side equals the cosecant of the angle opposite the second side times the sine of the angular length of the second side.

Formula

Csc[QuantityVariable["α", "Angle"]]*Sin[QuantityVariable["a", "Angle"]] == Csc[QuantityVariable["β", "Angle"]]*Sin[QuantityVariable["b", "Angle"]]

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

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Spherical Law of Sines"]
Out[1]=

Get the formula:

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

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Spherical Law of Sines"], {QuantityVariable["b","Angle"] -> Quantity[\[Pi]/2, "Radians"]}]
Out[3]=

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