Solve for Tension in 3-Cable System on 120 ft Tower Using Trigonometry

[r34racer01]

1. A 120 ft tower is being held by three cables in tension. Cable AO is in 1000
lb of tension. Find the tension in the other cables and the vertical force from
the tower if the whole system is at rest.

3. So using lots and lots of trig I was able to find most of the magnitudes, thetas, and phi's as you can see from the last 2 images. But now I'm lost from there. During office hrs. my prof. mentioned something about using unit vectors and then labeling the pts. A, B & C as coordinates A(-30,0,-20), b(-20,0,20), & c(40,0,10), but I don't see how those can help me. Any suggestions?

 

[nvn]

Hi, r34racer01. The PF rules state we are not allowed to tell you how to approach or solve your homework problem. You must list relevant equations yourself, and show your calculations to determine the forces; and then someone might check your math.