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Law of Sines

Calculate the angles in a generic triangle.

The "Law of Sines" can be used to calculate the angles of a triangle.

Law of cosines

The "Law of Sines" can be expressed as

$$  {a  \over sin A } = {b  \over sin B } = {c  \over sin C }   \tag{1}$$

where

a, b and c = length of sides in triangle (m, ft ...)

A, B and C = angles in the triangle (degrees)

Law of Sines Calculator

Eq. 1 can be modified to

$$  a = {b sin A \over sin B }  =  {c sin A \over sin C } \tag{1a}$$

$$  b = {a sin B \over sin A }  =  {c sin B \over sin C } \tag{1b}$$

$$  c = {a sin C \over sin A }  =  {b sin C \over sin B } \tag{1c}$$

This expression can also be handy:

$$  sin \frac{1}{2}A = \sqrt{{(s - b)(s - c) \over b c }}     \tag{2}$$

where

$$  s = \frac{1}{2}(a + b  + c)     \tag{3}$$

Related Topics

  • Mathematics

    Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

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