The tangent law of magnetism is a way to compare the strengths of two magnetic fields that are perpendicular to each other. If a compass or other magnet is subjected to a magnetic field B that is perpendicular to the horizontal magnetic field of the Earth (Bh), it will rest at an angle theta to the Earth's magnetic field. The relationship between the two magnetic fields is:
B = Bh(tan theta)
Because the tangent of the angle (the sine over the cosine) is the relevant factor here, the law is called the tangent law of magnetism.