Since the coordinate system is orthongonal, the Pythagorean theorem can be applied to determine the length of the cable. With the length of cable AB known, the aspect ratio of the side over the diagonal can be applied to determine the component forces. Note that the force components should sum vectorially to the original resultant force. The SRSS summation provided a good check of the calculation. Such checks should be done when ever you work through a problem where errors can occur.
Direction cosines are another useful method for determing rectangular components.
The use of direction cosines is illustrated in Figures 1.4.5 and 1.4.6.