Question

A boat owner pulls her boat into the dock shown, where thereare six capstans to which to tie the boat. She has three ropes. Shecan tie the boat from the boat's center (A) to any of the capstans(B through G) along the dotted arrows shown.
Suppose the owner has tied three ropes: one rope runs to A from B,another to A from D, and a final rope from A to F. The ropes aretied such that $F_{\rm AB} = F_{\rm AD}$ .

$MFS_1l_7_a.jpg$

The following notation is used in thisproblem: When a question refers to, for example, $F_AB_vec$ , this quantity is taken to mean the force acting on theboat due to the rope running to A from B, while $F_AB$ is the magnitude of that force.

What is the magnitude of the force provided by thethird rope, in terms of ?

A. F_ABCos(θ)

B. 2F_ABCos(θ)

C. 2F_ABSin(θ)

D.F_ABSin(θ)

I think its C. Am i right?