law of tangents
Quick Summary
The law of tangents is a trigonometric formula that relates two sides of a plane triangle to the tangents of the sum and difference of the angles opposite those sides. Specifically, for a triangle ABC with sides a, b, and c opposite angles A, B, and C respectively, the law states:1
[ \frac{a - b}{a + b} = \frac{\tan\frac{1}{2}(A - B)}{\tan\frac{1}{2}(A + B)} ]
This law is particularly useful for calculations involving logarithms. In trigonometry, the tangent of an angle in a right triangle is the ratio of the side opposite the angle to the adjacent side. The law of tangents is one of several trigonometric laws used to solve for unknown sides and angles in triangles, alongside the law of sines and the law of cosines.123
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