In addition to the tension T in cable BC, you want to know also the tension S in cable BD, I think.

In your sketch, I understand that the foot of the boom, point O, is at (0,0,0) of the (x,y,z) axes.

Also, the points B,C,D are all in the same z = 75cm plane....and this plane is horizontal.

And, point B is at (100cm, 0 , 75cm).

In the vertical (x,z) plane....for the compression U in the boom:

U is in the hypotenuse of the right triangle whose legs are 75cm vertical and 100cm horizontal.

At point B,

Break the U into its vertcal and horizontal components Uz and Ux respectively.

For equilibrium in the z-direction,

Uz = F = 500N.

By proportion, Uz / 75cm = Ux / 100cm

So, Ux = (100 / 75)Uz = (100 / 75)(500N) = 666.66667 N -------------------------------------**

This Ux will be supported by the combined tensions S and T in the two cables.

----------------------------------

In the horizontal z = 75cm plane:

For the tension T in the BC cable,

T is in the hypotenuse of the right triangle whose legs are 50cm and 100cm....so, the hypotenuse is sqrt(50^2 +100^2) =

111.8034 cm.

Break the T into its Tx and Ty components,

By proportion,

T / 111.8034 = Tx / 100 .......Tx = (100 / 111.8034)T = (0.89443)T

T / 111.8034 = Ty / 50 ......Ty = (50 / 111.8034)T = (0.44721)T

For the tension S in the BD cable,

S is in the hypotenuse of the right triangle whose legs are 75cm and 100cm....so, the hypotenuse is sqrt(75^2 +100^2) = 125cm.

Break the S into its Sx and Sy components,

By proportion,

S / 125 = Sx / 100 .......Sx = (100 / 125)S = (0.8)S

S / 125 = Sy / 75 ......Sy = (75 / 125)S = (0.6)S

For equilibrium in the y-direction at point B,

Ty = Sy

(0.44721)T = (0.6)S

T = (0.6 / 0.44721)S = (1.34165)S ------------------**

For eqilibrium in the x-direction,

Ux = Tx +Sx

666.66667 N = (0.89443)T +((0.8)S

Substituting (1.34165)S for T,

666.66667 = (0.89443)(1.34165 S) +(0.8)S

S = 666.6667 / 2.0

S = 333.33333 newtons ---------------------------------answer.

And, T = (1.34165)(333.33333) = 447.21667 newtons --------answer.