Calculate TCA and TCBSolutionTan alpha 20 48 041667 alpha

Calculate T_CA and T_CB.

Tan alpha = 20 / 48 = 0.41667

alpha = 22.62 deg

Tan beta = 55 / 48 = 1.1458

beta = 48.888 deg

Balancing forces in horizontal direction we get

Tca* sin alpha = Tcb * sin beta

Tca * 0.3846 = Tcb * 0.753

Tca = 1.96* Tcb

Balancing forces in vertical direction

Tca * cos alpha + Tcb * cos beta = 3600

1.96*Tcb * 0.923 + Tcb * 0.495 = 3600

Tcb = 1562.17 lb

Tca = 1.96* 1562.17

Tca = 3061.86 lb