Question

To support the tent, the tension in the rope AB must be 400 N. What are the tensions in the ropes AC, AD, and AE?

Answer 1

We develop the following position vectors

If we divide by the respective magnitudes we can develop the unit vectors that are parallel to these position vectors. 

The equilibrium equation is

TA_Be_AB + T_ACe_AC + T_ADe_AD + T_AEe_AE = 0.

If we break this up into components, we have

If we set T_AB = 400 N, we cans solve for the other tensions. The result is