Find Force Applied Horizontally to Displace 0.06kg Bob 0.10m

[Yashbhatt]

Homework Statement

A bob weighing 0.06 kg hangs vertically at the end of a string 0.30m long. Find the force which when applied horizontally. will pull the bob 0.10m aside from it's initial position.

Homework Equations

F = mg, F = ma

The Attempt at a Solution

The solution in the book says:

In the figure, F = ma, CA = 1.10 m; SO = SA = 0.30 m.
SC = (SA² - SC²)^1/2 = 2√2 / 10 m

As, mg/SC = F / CA = T/AS and then the value is calculated. I don't understand what is done after obtaining the value of SC.

 

[Orodruin]

What has to be true for the bob to be in equilibrium? How can you relate the forces acting on the bob to the right triangle of which you just computed the sides?
Hint: the pendulum string can only provide a force in throuh the tension in it, which is directed in the string direction.