Inverse Kinematics is used in computer graphics and robotics to control the posture of an articulated body. We introduce a new method utilising the law of cosines, which quickly determines the joint angles of a kinematic chain when given a target. Our method incurs a lower computational and rotational cost than Cyclic-Coordinate Descent (CCD), yet is also guaranteed to find a solution if one is available. Additionally it moves the upper joints of any kinematic chain first, thus ensuring a closer simulation of natural movement than CCD, which tends to overemphasise the movement of joints closer to the end-effector of the kinematic chain.