Posts tagged 'cosine law'

W.09 Law IV: The Cross Law & Quadrea-Spread Identity

In any triangle A_1 A_2 A_3 with non-null sides Q_1, Q_2 meeting with spread s_3 and cross c_3 = 1 - s_3 at vertex A_3, the quadrances satisfy (Q_1 + Q_2 - Q_3)^2 = 4 * Q_1 * Q_2 * (1 - s_3) = 4 * Q_1 * Q_2 * c_3, equivalently A(Q_1, Q_2, Q_3) = 4 * Q_1 * Q_2 * s_3.