Equilibrium Problem: Help Solving

[Matt1234]

Homework Statement

[PLAIN]http://img148.imageshack.us/img148/7880/95204069.jpg

Homework Equations

The Attempt at a Solution

Im not sure how to solve, i tried substitution but it gets really messy and trig identities are needed, some of which i don't know.

[PLAIN]http://img7.imageshack.us/img7/716/lastscantq.jpg

 

[Matt1234]

Can someone please help?

 

[rl.bhat]

You can apply the Lami's theorem.

For FBD-C

E/sin(150 + θ) = T(CB)/sin(90 + 30) ...(1)

For FBD - F

F/sin(135 - θ) = T(BC)/sin(90 + 45)...(2)

T(CB) = - T(BC)

E*sin(90 + 30)/sin(150 + θ) = T(CB)

F*sin(90 + 45)/sin(135 - θ) = T(BC)

E*sin(90 + 30)/sin(150 + θ) = - F*sin(90 + 45)/sin(135 - θ)

Substitute the known values.

Using sin(A+B) =sinAcosB + cosAsinB

and sin(A-B) = sinAcosB - cosAsinB

Find cosθ in terms of sinθ.

Using the identity cos^2(θ) = 1 - sin^2(θ), form a quadratic equation and then solve for sinθ and hence θ.