Solving Statics Problem: Equilibrium of Forces

[619313]

I have having trouble solving this statics problem, I sum up the forces and have

C*cos(30) - B*cos(phi) = 0 in the positive x direction
and
C*sin(30) + B*sin(phi) - D =0 in the positive y direction

B = 275 lbs and D = 300lbs
I need to solve for C and phi, I have tried substitution, division, not matrices because it wouldn't work

 

[rl.bhat]

C*cos(30) = B*cos(phi)...(1)
C*sin(30) = - B*sin(phi) + D ...(2)
Divide (2) by (1).You get
tan(30) = B*cosφ/(B*sinφ - D)
Square both the sides. Write cos^2(φ) = 1 - sin^2(φ) and solve the quadratics to find φ.

 

[619313]

Thanks for the reply,

I divided (2) by (1) but I have

Tan(30) = (-B*sin(φ) + D)/ (B*cos(φ))

Am I missing something?

 

[rl.bhat]

No.
Now square both sides. And simplify.