Angle From Law of Sines

The Angle of a Triangle (Law of Sines) calculator computes the angle of one side based on the opposite angle and the length of the other two sides.

INSTRUCTIONS: Choose units and enter the following:

• (β) Angle opposite of side b
• (a) Side a
• (b) Side b

Angle of a Triangle (α): The calculator returns the angle in radians.  However, this can be automatically converted to compatible units via the pull-down menu

The Math / Science

The law of sines reflects that any arbitrary triangle with sides a, b, and c and angles opposite those sides α, β and γ have the following relationship between it's angles and sides:  sin(α) / a = sin(β )/ b = sin(γ) / c.  Thus given any pair of angles and an opposite side, or any pair of sides and an opposite angle, you can compute the complimentary opposite side or angle respectively.

α = arcsin( (sin(β) * a) / b  )