# 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

*a ^{2} + b^{2} = c^{2} (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((b ^{2} + c^{2} - a^{2}) / (2 b c)) (4a)*

*B = arccos((a ^{2} + c^{2} - b^{2}) / (2 a c)) (4b)*

*C = arccos((a ^{2} + b^{2} - c^{2}) / (2 a b)) (4c)*