# Law of Sines

## Calculate the angles in a generic triangle.

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

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 *

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