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# Law of Tangents

## Triangles and law of tangents

The "Law of Tangents" can be used to calculate the angles or sides of a triangle. ### Law of Tangents

The "Law of Tangents" can be expressed as

(a + b) / (a - b) = tan 1/2 (A + B) / tan 1/2 (A - B)                         (1)

where

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

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

### Pythagorean theorem

The Pythagorean theorem can be expressed as

a2 + b2 = c2                 (2)

### Law of sines

The Law of sines can be expressed as

a / sin(A) = b / sin(B) = c / sin(C)                (3)

### Angles

If the length of all three sides in the triangle are known - the angles can be calculated as

A = arccos((b2 + c2 - a2) / (2 b c))                     (4a)

B = arccos((a2 + c2 - b2) / (2 a c))                     (4b)

C = arccos((a2 + b2 - c2) / (2 a b))                     (4c)

## Related Topics

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

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## Citation

• Engineering ToolBox, (2020). Law of Tangents. [online] Available at: https://www.engineeringtoolbox.com/law-tangents-d_2178.html [Accessed Day Mo. Year].

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