▽ Law of Tangents

While less known than the Laws of Sines/Cosines, the Law of Tangents provides elegant solutions for specific triangle configurations.

The Formula

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

Where:
a, b = sides opposite angles A, B

When to Apply

Calculation Example

Given triangle with:
a = 6, b = 4, C = 60°
Find angles A and B

Solution:
1. (6-4)/(6+4) = tan[(A-B)/2]/tan[(A+B)/2]
2. A+B = 120° ⇒ (A+B)/2 = 60°
3. Solve for (A-B) then combine with A+B=120°

Historical Significance

Before calculators, this law was preferred because:

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