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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. 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

a (m, ft ....)

b (m, ft ....)

A (degrees)

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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## Citation

• Engineering ToolBox, (2013). Law of Sines. [online] Available at: https://www.engineeringtoolbox.com/law-of-sines-d_1858.html [Accessed Day Mo. Year].

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