Problem $1$:

Three cables are used to tether a balloon as shown. The vertical force $P$ exerted by

balloon at the point A and knowing that the tension force TAD in the cable AD is $300$ N $.$

Draw the force diagram of the joint $A$;

Determine the unit vectors of $T_{AB},T_{AC},$ and $T_{AD}$;

Form three equilibrium equations in scalar form for solving the magnitude of tension

forces $T_{AB},T_{AC},$ and the vertical force $P$;

Solve the tension forces $T_{AB},T_{AC},$ and the vertical force $P.$

Hint: This is a $3-$D concurrent force system at A in equilibrium